Index
stringlengths 1
5
| Challenge
stringlengths 41
1.55k
| Answer in Latex
stringclasses 122
values | Answer in Sympy
stringlengths 1
774
| Variation
stringclasses 31
values | Source
stringclasses 61
values |
|---|---|---|---|---|---|
401
|
Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(9997025\right) n \cdot ( \left(3399363\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(8635398\right) n \cdot ( \left(3399363\right) x)^n\right$
|
Sum(n*x**n*(n**2 - 1)*3399363**n, (n, 2, oo))*8635398*9997025/6
|
Numeric-All-7
|
U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a
|
|
402
|
Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(50849136\right) n \cdot ( \left(49317708\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(38518091\right) n \cdot ( \left(49317708\right) x)^n\right$
|
Sum(n*x**n*(n**2 - 1)*49317708**n, (n, 2, oo))*38518091*50849136/6
|
Numeric-All-8
|
U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a
|
|
403
|
Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(597140185\right) n \cdot ( \left(908557767\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(130111075\right) n \cdot ( \left(908557767\right) x)^n\right$
|
Sum(n*x**n*(n**2 - 1)*908557767**n, (n, 2, oo))*130111075*597140185/6
|
Numeric-All-9
|
U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a
|
|
404
|
Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(7136646496\right) n \cdot ( \left(3240980819\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(3618373856\right) n \cdot ( \left(3240980819\right) x)^n\right$
|
Sum(n*x**n*(n**2 - 1)*3240980819**n, (n, 2, oo))*3618373856*7136646496/6
|
Numeric-All-10
|
U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a
|
|
405
|
Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot (F x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left(B n \cdot (F x)^n\right$
|
B*Sum(F**n*n*x**n*(n**2 - 1), (n, 2, oo))/6
|
Symbolic-2
|
U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a
|
|
406
|
Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left(A n \cdot (F x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot (F x)^n\right$
|
A*Sum(F**n*n*x**n*(n**2 - 1), (n, 2, oo))/6
|
Symbolic-2
|
U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a
|
|
407
|
Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left(A n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left(B n \cdot ( x)^n\right$
|
A*B*Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6
|
Symbolic-2
|
U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a
|
|
408
|
Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot (F x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot (F x)^n\right$
|
Sum(F**n*n*x**n*(n**2 - 1), (n, 2, oo))/6
|
Symbolic-1
|
U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a
|
|
409
|
Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left(B n \cdot ( x)^n\right$
|
B*Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6
|
Symbolic-1
|
U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a
|
|
410
|
Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left(A n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$
|
A*Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6
|
Symbolic-1
|
U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a
|
|
411
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
412
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
413
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
414
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
415
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
416
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
417
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
418
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
419
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
420
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
421
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
422
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
423
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
424
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
425
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
426
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
427
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
428
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
429
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
430
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
431
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
432
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
433
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
434
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
435
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
436
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
437
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
438
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
439
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
440
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
441
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
442
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
443
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
444
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
445
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
446
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
447
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
448
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
449
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
450
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
451
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
452
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
453
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
454
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
455
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
456
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
457
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
458
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
459
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
460
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
461
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
462
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
463
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
464
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
465
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
466
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
467
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
468
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
469
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
470
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
471
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
472
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
473
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
474
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
475
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
476
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
477
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
478
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
479
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
480
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
481
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
482
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
483
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
484
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
485
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
486
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
487
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
488
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
489
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
490
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
491
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
492
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
493
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
494
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
495
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
496
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
497
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
498
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
499
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Easy
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
|
500
|
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$
|
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
|
Equivalence-All-Hard
|
U-Math
sequences_series
f89bd354-18c9-4f31-b91f-cf6421e24921
|
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