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 |
|---|---|---|---|---|---|
701
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) e^{ \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x} \cdot \cos( \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
702
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) e^{ \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x} \cdot \cos( \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
703
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) e^{ \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x} \cdot \cos( \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
704
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) e^{ \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x} \cdot \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
705
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) e^{ \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x} \cdot \cos( \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
706
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) e^{ \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x} \cdot \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
707
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) e^{ \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x} \cdot \cos( \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
708
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) e^{ \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x} \cdot \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
709
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) e^{ \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x} \cdot \cos( \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
710
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) e^{ \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x} \cdot \cos( \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
711
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) e^{ \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x} \cdot \cos( \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
712
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) e^{ \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x} \cdot \cos( \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
713
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) e^{ \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x} \cdot \cos( \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
714
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) e^{ \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x} \cdot \cos( \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
715
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) e^{ \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x} \cdot \cos( \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
716
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) e^{ \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x} \cdot \cos( \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
717
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) e^{ \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x} \cdot \cos( \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
718
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) e^{ \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x} \cdot \cos( \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
719
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) e^{ \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x} \cdot \cos( \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
720
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) e^{ \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x} \cdot \cos( \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
721
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) e^{ \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x} \cdot \cos( \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
722
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) e^{ \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x} \cdot \cos( \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
723
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) e^{ \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x} \cdot \cos( \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
724
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) e^{ \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x} \cdot \cos( \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
725
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) e^{ \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x} \cdot \cos( \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
726
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) e^{ \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x} \cdot \cos( \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-All-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
727
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x} \cdot \cos( x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
728
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x} \cdot \cos( x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
729
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x} \cdot \cos( x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
730
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x} \cdot \cos( x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
731
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x} \cdot \cos( x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
732
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x} \cdot \cos( x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
733
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x} \cdot \cos( x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
734
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x} \cdot \cos( x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
735
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) x} \cdot \cos( x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
736
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) x} \cdot \cos( x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
737
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ \left(9\right) x} \cdot \cos( x)$
|
(x**4*(1 - 6*9**2 + 9**4) + 4*x**3*9*(-3 + 9**2) + 12*x**2*(-1 + 9**2) + 24*x*9 + 24)/24
|
Numeric-One-1
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
738
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ \left(59\right) x} \cdot \cos( x)$
|
(x**4*(1 - 6*59**2 + 59**4) + 4*x**3*59*(-3 + 59**2) + 12*x**2*(-1 + 59**2) + 24*x*59 + 24)/24
|
Numeric-One-2
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
739
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ \left(273\right) x} \cdot \cos( x)$
|
(x**4*(1 - 6*273**2 + 273**4) + 4*x**3*273*(-3 + 273**2) + 12*x**2*(-1 + 273**2) + 24*x*273 + 24)/24
|
Numeric-One-3
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
740
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ \left(7659\right) x} \cdot \cos( x)$
|
(x**4*(1 - 6*7659**2 + 7659**4) + 4*x**3*7659*(-3 + 7659**2) + 12*x**2*(-1 + 7659**2) + 24*x*7659 + 24)/24
|
Numeric-One-4
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
741
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ \left(91120\right) x} \cdot \cos( x)$
|
(x**4*(1 - 6*91120**2 + 91120**4) + 4*x**3*91120*(-3 + 91120**2) + 12*x**2*(-1 + 91120**2) + 24*x*91120 + 24)/24
|
Numeric-One-5
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
742
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ \left(905850\right) x} \cdot \cos( x)$
|
(x**4*(1 - 6*905850**2 + 905850**4) + 4*x**3*905850*(-3 + 905850**2) + 12*x**2*(-1 + 905850**2) + 24*x*905850 + 24)/24
|
Numeric-One-6
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
743
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ \left(2464365\right) x} \cdot \cos( x)$
|
(x**4*(1 - 6*2464365**2 + 2464365**4) + 4*x**3*2464365*(-3 + 2464365**2) + 12*x**2*(-1 + 2464365**2) + 24*x*2464365 + 24)/24
|
Numeric-One-7
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
744
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ \left(18016479\right) x} \cdot \cos( x)$
|
(x**4*(1 - 6*18016479**2 + 18016479**4) + 4*x**3*18016479*(-3 + 18016479**2) + 12*x**2*(-1 + 18016479**2) + 24*x*18016479 + 24)/24
|
Numeric-One-8
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
745
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ \left(303850321\right) x} \cdot \cos( x)$
|
(x**4*(1 - 6*303850321**2 + 303850321**4) + 4*x**3*303850321*(-3 + 303850321**2) + 12*x**2*(-1 + 303850321**2) + 24*x*303850321 + 24)/24
|
Numeric-One-9
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
746
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ \left(8280308318\right) x} \cdot \cos( x)$
|
(x**4*(1 - 6*8280308318**2 + 8280308318**4) + 4*x**3*8280308318*(-3 + 8280308318**2) + 12*x**2*(-1 + 8280308318**2) + 24*x*8280308318 + 24)/24
|
Numeric-One-10
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
747
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ x} \cdot \cos( \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
748
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ x} \cdot \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
749
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ x} \cdot \cos( \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
750
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ x} \cdot \cos( \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
751
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ x} \cdot \cos( \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
752
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ x} \cdot \cos( \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
753
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ x} \cdot \cos( \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
754
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ x} \cdot \cos( \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
755
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ x} \cdot \cos( \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
756
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ x} \cdot \cos( \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
757
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ x} \cdot \cos( \left(7\right) x)$
|
(x**4*(1 - 6*7**2 + 7**4) + 4*x**3*(1 - 3*7**2) + 12*x**2*(1 - 7**2) + 24*x + 24)/24
|
Numeric-One-1
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
758
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ x} \cdot \cos( \left(44\right) x)$
|
(x**4*(1 - 6*44**2 + 44**4) + 4*x**3*(1 - 3*44**2) + 12*x**2*(1 - 44**2) + 24*x + 24)/24
|
Numeric-One-2
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
759
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ x} \cdot \cos( \left(108\right) x)$
|
(x**4*(1 - 6*108**2 + 108**4) + 4*x**3*(1 - 3*108**2) + 12*x**2*(1 - 108**2) + 24*x + 24)/24
|
Numeric-One-3
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
760
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ x} \cdot \cos( \left(3099\right) x)$
|
(x**4*(1 - 6*3099**2 + 3099**4) + 4*x**3*(1 - 3*3099**2) + 12*x**2*(1 - 3099**2) + 24*x + 24)/24
|
Numeric-One-4
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
761
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ x} \cdot \cos( \left(48751\right) x)$
|
(x**4*(1 - 6*48751**2 + 48751**4) + 4*x**3*(1 - 3*48751**2) + 12*x**2*(1 - 48751**2) + 24*x + 24)/24
|
Numeric-One-5
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
762
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ x} \cdot \cos( \left(400382\right) x)$
|
(x**4*(1 - 6*400382**2 + 400382**4) + 4*x**3*(1 - 3*400382**2) + 12*x**2*(1 - 400382**2) + 24*x + 24)/24
|
Numeric-One-6
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
763
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ x} \cdot \cos( \left(1631844\right) x)$
|
(x**4*(1 - 6*1631844**2 + 1631844**4) + 4*x**3*(1 - 3*1631844**2) + 12*x**2*(1 - 1631844**2) + 24*x + 24)/24
|
Numeric-One-7
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
764
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ x} \cdot \cos( \left(25137196\right) x)$
|
(x**4*(1 - 6*25137196**2 + 25137196**4) + 4*x**3*(1 - 3*25137196**2) + 12*x**2*(1 - 25137196**2) + 24*x + 24)/24
|
Numeric-One-8
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
765
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ x} \cdot \cos( \left(996206616\right) x)$
|
(x**4*(1 - 6*996206616**2 + 996206616**4) + 4*x**3*(1 - 3*996206616**2) + 12*x**2*(1 - 996206616**2) + 24*x + 24)/24
|
Numeric-One-9
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
766
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ x} \cdot \cos( \left(8078512087\right) x)$
|
(x**4*(1 - 6*8078512087**2 + 8078512087**4) + 4*x**3*(1 - 3*8078512087**2) + 12*x**2*(1 - 8078512087**2) + 24*x + 24)/24
|
Numeric-One-10
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
767
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) e^{ x} \cdot \cos( x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
768
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) e^{ x} \cdot \cos( x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
769
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) e^{ x} \cdot \cos( x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
770
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) e^{ x} \cdot \cos( x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
771
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) e^{ x} \cdot \cos( x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
772
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) e^{ x} \cdot \cos( x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
773
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) e^{ x} \cdot \cos( x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
774
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) e^{ x} \cdot \cos( x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
775
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) e^{ x} \cdot \cos( x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Easy
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
776
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) e^{ x} \cdot \cos( x)$
|
-x**4/6 - x**3/3 + x + 1
|
Equivalence-One-Hard
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
777
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(6\right) e^{ x} \cdot \cos( x)$
|
(-4*x**4 - 8*x**3 + 24*x + 24)*6/24
|
Numeric-One-1
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
778
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(45\right) e^{ x} \cdot \cos( x)$
|
(-4*x**4 - 8*x**3 + 24*x + 24)*45/24
|
Numeric-One-2
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
779
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(778\right) e^{ x} \cdot \cos( x)$
|
(-4*x**4 - 8*x**3 + 24*x + 24)*778/24
|
Numeric-One-3
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
780
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(4330\right) e^{ x} \cdot \cos( x)$
|
(-4*x**4 - 8*x**3 + 24*x + 24)*4330/24
|
Numeric-One-4
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
781
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(31410\right) e^{ x} \cdot \cos( x)$
|
(-4*x**4 - 8*x**3 + 24*x + 24)*31410/24
|
Numeric-One-5
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
782
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(327629\right) e^{ x} \cdot \cos( x)$
|
(-4*x**4 - 8*x**3 + 24*x + 24)*327629/24
|
Numeric-One-6
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
783
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(8744282\right) e^{ x} \cdot \cos( x)$
|
(-4*x**4 - 8*x**3 + 24*x + 24)*8744282/24
|
Numeric-One-7
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
784
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(16956066\right) e^{ x} \cdot \cos( x)$
|
(-4*x**4 - 8*x**3 + 24*x + 24)*16956066/24
|
Numeric-One-8
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
785
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(231539438\right) e^{ x} \cdot \cos( x)$
|
(-4*x**4 - 8*x**3 + 24*x + 24)*231539438/24
|
Numeric-One-9
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
786
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(9876936495\right) e^{ x} \cdot \cos( x)$
|
(-4*x**4 - 8*x**3 + 24*x + 24)*9876936495/24
|
Numeric-One-10
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
787
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(3\right) e^{ \left(4\right) x} \cdot \cos( \left(3\right) x)$
|
3*(x**4*(-6*3**2*4**2 + 3**4 + 4**4) + 4*x**3*4*(-3*3**2 + 4**2) + 12*x**2*(-3**2 + 4**2) + 24*x*4 + 24)/24
|
Numeric-All-1
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
788
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(67\right) e^{ \left(22\right) x} \cdot \cos( \left(34\right) x)$
|
67*(x**4*(22**4 - 6*34**2*22**2 + 34**4) + 4*x**3*22*(22**2 - 3*34**2) + 12*x**2*(22**2 - 34**2) + 24*x*22 + 24)/24
|
Numeric-All-2
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
789
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(598\right) e^{ \left(209\right) x} \cdot \cos( \left(586\right) x)$
|
598*(x**4*(209**4 - 6*586**2*209**2 + 586**4) + 4*x**3*209*(209**2 - 3*586**2) + 12*x**2*(209**2 - 586**2) + 24*x*209 + 24)/24
|
Numeric-All-3
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
790
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(7767\right) e^{ \left(6811\right) x} \cdot \cos( \left(5465\right) x)$
|
7767*(x**4*(-6*5465**2*6811**2 + 5465**4 + 6811**4) + 4*x**3*6811*(-3*5465**2 + 6811**2) + 12*x**2*(-5465**2 + 6811**2) + 24*x*6811 + 24)/24
|
Numeric-All-4
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
791
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(26242\right) e^{ \left(41239\right) x} \cdot \cos( \left(51516\right) x)$
|
26242*(x**4*(41239**4 - 6*51516**2*41239**2 + 51516**4) + 4*x**3*41239*(41239**2 - 3*51516**2) + 12*x**2*(41239**2 - 51516**2) + 24*x*41239 + 24)/24
|
Numeric-All-5
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
792
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(618448\right) e^{ \left(497466\right) x} \cdot \cos( \left(223098\right) x)$
|
618448*(x**4*(-6*223098**2*497466**2 + 223098**4 + 497466**4) + 4*x**3*497466*(-3*223098**2 + 497466**2) + 12*x**2*(-223098**2 + 497466**2) + 24*x*497466 + 24)/24
|
Numeric-All-6
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
793
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(1064384\right) e^{ \left(5002755\right) x} \cdot \cos( \left(3759905\right) x)$
|
1064384*(x**4*(-6*3759905**2*5002755**2 + 3759905**4 + 5002755**4) + 4*x**3*5002755*(-3*3759905**2 + 5002755**2) + 12*x**2*(-3759905**2 + 5002755**2) + 24*x*5002755 + 24)/24
|
Numeric-All-7
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
794
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(34506787\right) e^{ \left(31740135\right) x} \cdot \cos( \left(63722038\right) x)$
|
34506787*(x**4*(31740135**4 - 6*63722038**2*31740135**2 + 63722038**4) + 4*x**3*31740135*(31740135**2 - 3*63722038**2) + 12*x**2*(31740135**2 - 63722038**2) + 24*x*31740135 + 24)/24
|
Numeric-All-8
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
795
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(962444551\right) e^{ \left(661340633\right) x} \cdot \cos( \left(108175673\right) x)$
|
962444551*(x**4*(-6*108175673**2*661340633**2 + 108175673**4 + 661340633**4) + 4*x**3*661340633*(-3*108175673**2 + 661340633**2) + 12*x**2*(-108175673**2 + 661340633**2) + 24*x*661340633 + 24)/24
|
Numeric-All-9
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
796
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = \left(5354662213\right) e^{ \left(5781904323\right) x} \cdot \cos( \left(5699748724\right) x)$
|
5354662213*(x**4*(-6*5699748724**2*5781904323**2 + 5699748724**4 + 5781904323**4) + 4*x**3*5781904323*(-3*5699748724**2 + 5781904323**2) + 12*x**2*(-5699748724**2 + 5781904323**2) + 24*x*5781904323 + 24)/24
|
Numeric-All-10
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
797
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = F e^{ x} \cdot \cos(B x)$
|
F*(x**4*(B**4 - 6*B**2 + 1) + 4*x**3*(1 - 3*B**2) + 12*x**2*(1 - B**2) + 24*x + 24)/24
|
Symbolic-2
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
798
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = F e^{A x} \cdot \cos( x)$
|
F*(4*A*x**3*(A**2 - 3) + 24*A*x + x**4*(A**4 - 6*A**2 + 1) + 12*x**2*(A**2 - 1) + 24)/24
|
Symbolic-2
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
799
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{A x} \cdot \cos(B x)$
|
A*x**3*(A**2 - 3*B**2)/6 + A*x + x**4*(A**4 - 6*A**2*B**2 + B**4)/24 + x**2*(A**2 - B**2)/2 + 1
|
Symbolic-2
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
800
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = F e^{ x} \cdot \cos( x)$
|
F*(-4*x**4 - 8*x**3 + 24*x + 24)/24
|
Symbolic-1
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
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