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 |
|---|---|---|---|---|---|
801
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{ x} \cdot \cos(B x)$
|
x**4*(B**4 - 6*B**2 + 1)/24 + x**3*(1 - 3*B**2)/6 + x**2*(1 - B**2)/2 + x + 1
|
Symbolic-1
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
802
|
Compute the terms up to order 4 ($x^4$) of the Maclaurin series of $f(x) = e^{A x} \cdot \cos( x)$
|
A*x**3*(A**2 - 3)/6 + A*x + x**4*(A**4 - 6*A**2 + 1)/24 + x**2*(A**2 - 1)/2 + 1
|
Symbolic-1
|
U-Math
sequences_series
d1fe21df-ee7f-40c2-9655-6bd6a7a23ff1
|
|
803
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)+4) \csc ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)}{5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^3}-\frac{6}{5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^4}$
|
1/150
|
Equivalence-All-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
804
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)+4) \csc ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)}{5 \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^3}-\frac{6}{5 \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^4}$
|
1/150
|
Equivalence-All-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
805
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)+4) \csc ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)}{5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^3}-\frac{6}{5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^4}$
|
1/150
|
Equivalence-All-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
806
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)+4) \csc ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)}{5 \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^3}-\frac{6}{5 \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^4}$
|
1/150
|
Equivalence-All-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
807
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)+4) \csc ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)}{5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^3}-\frac{6}{5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^4}$
|
1/150
|
Equivalence-All-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
808
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)+4) \csc ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)}{5 \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^3}-\frac{6}{5 \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^4}$
|
1/150
|
Equivalence-All-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
809
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)+4) \csc ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)}{5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^3}-\frac{6}{5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^4}$
|
1/150
|
Equivalence-All-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
810
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)+4) \csc ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)}{5 \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)^3}-\frac{6}{5 \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)^4}$
|
1/150
|
Equivalence-All-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
811
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)+4) \csc ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)}{5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^3}-\frac{6}{5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^4}$
|
1/150
|
Equivalence-All-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
812
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)+4) \csc ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)}{5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)^3}-\frac{6}{5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)^4}$
|
1/150
|
Equivalence-All-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
813
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)+4) \csc ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)}{5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^3}-\frac{6}{5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^4}$
|
1/150
|
Equivalence-All-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
814
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)+4) \csc ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)}{5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^3}-\frac{6}{5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^4}$
|
1/150
|
Equivalence-All-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
815
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)+4) \csc ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)}{5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^3}-\frac{6}{5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^4}$
|
1/150
|
Equivalence-All-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
816
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)+4) \csc ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)}{5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^3}-\frac{6}{5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^4}$
|
1/150
|
Equivalence-All-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
817
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)+4) \csc ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)}{5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^3}-\frac{6}{5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^4}$
|
1/150
|
Equivalence-All-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
818
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)+4) \csc ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)}{5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)^3}-\frac{6}{5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)^4}$
|
1/150
|
Equivalence-All-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
819
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)+4) \csc ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)}{5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^3}-\frac{6}{5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^4}$
|
1/150
|
Equivalence-All-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
820
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)+4) \csc ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)}{5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)^3}-\frac{6}{5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)^4}$
|
1/150
|
Equivalence-All-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
821
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)+4) \csc ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)}{5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^3}-\frac{6}{5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^4}$
|
1/150
|
Equivalence-All-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
822
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)+4) \csc ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)}{5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^3}-\frac{6}{5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^4}$
|
1/150
|
Equivalence-All-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
823
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)+4) \csc ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)}{5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^3}-\frac{6}{5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^4}$
|
1/150
|
Equivalence-All-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
824
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)+4) \csc ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)}{5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^3}-\frac{6}{5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^4}$
|
1/150
|
Equivalence-All-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
825
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)+4) \csc ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)}{5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^3}-\frac{6}{5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^4}$
|
1/150
|
Equivalence-All-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
826
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)+4) \csc ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)}{5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)^3}-\frac{6}{5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)^4}$
|
1/150
|
Equivalence-All-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
827
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)+4) \csc ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)}{5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^3}-\frac{6}{5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^4}$
|
1/150
|
Equivalence-All-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
828
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)+4) \csc ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)}{5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)^3}-\frac{6}{5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)^4}$
|
1/150
|
Equivalence-All-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
829
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)+4) \csc ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)}{5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^3}-\frac{6}{5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^4}$
|
1/150
|
Equivalence-All-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
830
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)+4) \csc ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)}{5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^3}-\frac{6}{5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^4}$
|
1/150
|
Equivalence-All-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
831
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)+4) \csc ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)}{5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^3}-\frac{6}{5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^4}$
|
1/150
|
Equivalence-All-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
832
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)+4) \csc ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)}{5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^3}-\frac{6}{5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^4}$
|
1/150
|
Equivalence-All-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
833
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)+4) \csc ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)}{5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^3}-\frac{6}{5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^4}$
|
1/150
|
Equivalence-All-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
834
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)+4) \csc ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)}{5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)^3}-\frac{6}{5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)^4}$
|
1/150
|
Equivalence-All-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
835
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)+4) \csc ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)}{5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^3}-\frac{6}{5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^4}$
|
1/150
|
Equivalence-All-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
836
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)+4) \csc ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)}{5 \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)^3}-\frac{6}{5 \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)^4}$
|
1/150
|
Equivalence-All-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
837
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)+4) \csc ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)}{5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^3}-\frac{6}{5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^4}$
|
1/150
|
Equivalence-All-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
838
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)+4) \csc ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)}{5 \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^3}-\frac{6}{5 \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^4}$
|
1/150
|
Equivalence-All-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
839
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)+4) \csc ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)}{5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^3}-\frac{6}{5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^4}$
|
1/150
|
Equivalence-All-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
840
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)+4) \csc ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)}{5 \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^3}-\frac{6}{5 \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^4}$
|
1/150
|
Equivalence-All-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
841
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)+4) \csc ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)}{5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^3}-\frac{6}{5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^4}$
|
1/150
|
Equivalence-All-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
842
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)+4) \csc ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)}{5 \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^3}-\frac{6}{5 \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^4}$
|
1/150
|
Equivalence-All-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
843
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( x)+4) \csc ( x)}{5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) ( x)^3}-\frac{6}{5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) ( x)^4}$
|
1/150
|
Equivalence-One-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
844
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( x)+4) \csc ( x)}{5 \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) ( x)^3}-\frac{6}{5 \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) ( x)^4}$
|
1/150
|
Equivalence-One-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
845
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( x)+4) \csc ( x)}{5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) ( x)^3}-\frac{6}{5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) ( x)^4}$
|
1/150
|
Equivalence-One-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
846
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( x)+4) \csc ( x)}{5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) ( x)^3}-\frac{6}{5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) ( x)^4}$
|
1/150
|
Equivalence-One-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
847
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( x)+4) \csc ( x)}{5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) ( x)^3}-\frac{6}{5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) ( x)^4}$
|
1/150
|
Equivalence-One-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
848
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( x)+4) \csc ( x)}{5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) ( x)^3}-\frac{6}{5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) ( x)^4}$
|
1/150
|
Equivalence-One-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
849
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( x)+4) \csc ( x)}{5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) ( x)^3}-\frac{6}{5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) ( x)^4}$
|
1/150
|
Equivalence-One-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
850
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( x)+4) \csc ( x)}{5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) ( x)^3}-\frac{6}{5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) ( x)^4}$
|
1/150
|
Equivalence-One-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
851
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( x)+4) \csc ( x)}{5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) ( x)^3}-\frac{6}{5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) ( x)^4}$
|
1/150
|
Equivalence-One-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
852
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( x)+4) \csc ( x)}{5 \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) ( x)^3}-\frac{6}{5 \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) ( x)^4}$
|
1/150
|
Equivalence-One-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
853
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( x)+4) \csc ( x)}{5 \left(1\right) ( x)^3}-\frac{6}{5 \left(1\right) ( x)^4}$
|
1**(-1)/150
|
Numeric-One-1
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
854
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( x)+4) \csc ( x)}{5 \left(19\right) ( x)^3}-\frac{6}{5 \left(19\right) ( x)^4}$
|
19**(-1)/150
|
Numeric-One-2
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
855
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( x)+4) \csc ( x)}{5 \left(290\right) ( x)^3}-\frac{6}{5 \left(290\right) ( x)^4}$
|
290**(-1)/150
|
Numeric-One-3
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
856
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( x)+4) \csc ( x)}{5 \left(9287\right) ( x)^3}-\frac{6}{5 \left(9287\right) ( x)^4}$
|
9287**(-1)/150
|
Numeric-One-4
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
857
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( x)+4) \csc ( x)}{5 \left(38103\right) ( x)^3}-\frac{6}{5 \left(38103\right) ( x)^4}$
|
38103**(-1)/150
|
Numeric-One-5
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
858
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( x)+4) \csc ( x)}{5 \left(441344\right) ( x)^3}-\frac{6}{5 \left(441344\right) ( x)^4}$
|
441344**(-1)/150
|
Numeric-One-6
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
859
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( x)+4) \csc ( x)}{5 \left(4721836\right) ( x)^3}-\frac{6}{5 \left(4721836\right) ( x)^4}$
|
4721836**(-1)/150
|
Numeric-One-7
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
860
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( x)+4) \csc ( x)}{5 \left(18419205\right) ( x)^3}-\frac{6}{5 \left(18419205\right) ( x)^4}$
|
18419205**(-1)/150
|
Numeric-One-8
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
861
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( x)+4) \csc ( x)}{5 \left(964636872\right) ( x)^3}-\frac{6}{5 \left(964636872\right) ( x)^4}$
|
964636872**(-1)/150
|
Numeric-One-9
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
862
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( x)+4) \csc ( x)}{5 \left(6724428116\right) ( x)^3}-\frac{6}{5 \left(6724428116\right) ( x)^4}$
|
6724428116**(-1)/150
|
Numeric-One-10
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
863
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)+4) \csc ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)}{5 ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^3}-\frac{6}{5 ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^4}$
|
1/150
|
Equivalence-One-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
864
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)+4) \csc ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)}{5 ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)^3}-\frac{6}{5 ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)^4}$
|
1/150
|
Equivalence-One-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
865
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)+4) \csc ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)}{5 ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^3}-\frac{6}{5 ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^4}$
|
1/150
|
Equivalence-One-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
866
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)+4) \csc ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)}{5 ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^3}-\frac{6}{5 ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^4}$
|
1/150
|
Equivalence-One-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
867
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)+4) \csc ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)}{5 ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^3}-\frac{6}{5 ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^4}$
|
1/150
|
Equivalence-One-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
868
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)+4) \csc ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)}{5 ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^3}-\frac{6}{5 ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^4}$
|
1/150
|
Equivalence-One-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
869
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)+4) \csc ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)}{5 ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^3}-\frac{6}{5 ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^4}$
|
1/150
|
Equivalence-One-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
870
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)+4) \csc ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)}{5 ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^3}-\frac{6}{5 ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^4}$
|
1/150
|
Equivalence-One-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
871
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)+4) \csc ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)}{5 ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^3}-\frac{6}{5 ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^4}$
|
1/150
|
Equivalence-One-Easy
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
872
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)+4) \csc ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)}{5 ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)^3}-\frac{6}{5 ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)^4}$
|
1/150
|
Equivalence-One-Hard
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
873
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(4\right) x)+4) \csc ( \left(4\right) x)}{5 ( \left(4\right) x)^3}-\frac{6}{5 ( \left(4\right) x)^4}$
|
1/150
|
Numeric-One-1
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
874
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(42\right) x)+4) \csc ( \left(42\right) x)}{5 ( \left(42\right) x)^3}-\frac{6}{5 ( \left(42\right) x)^4}$
|
1/150
|
Numeric-One-2
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
875
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(660\right) x)+4) \csc ( \left(660\right) x)}{5 ( \left(660\right) x)^3}-\frac{6}{5 ( \left(660\right) x)^4}$
|
1/150
|
Numeric-One-3
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
876
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(7545\right) x)+4) \csc ( \left(7545\right) x)}{5 ( \left(7545\right) x)^3}-\frac{6}{5 ( \left(7545\right) x)^4}$
|
1/150
|
Numeric-One-4
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
877
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(21958\right) x)+4) \csc ( \left(21958\right) x)}{5 ( \left(21958\right) x)^3}-\frac{6}{5 ( \left(21958\right) x)^4}$
|
1/150
|
Numeric-One-5
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
878
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(170983\right) x)+4) \csc ( \left(170983\right) x)}{5 ( \left(170983\right) x)^3}-\frac{6}{5 ( \left(170983\right) x)^4}$
|
1/150
|
Numeric-One-6
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
879
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(3684654\right) x)+4) \csc ( \left(3684654\right) x)}{5 ( \left(3684654\right) x)^3}-\frac{6}{5 ( \left(3684654\right) x)^4}$
|
1/150
|
Numeric-One-7
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
880
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(31500120\right) x)+4) \csc ( \left(31500120\right) x)}{5 ( \left(31500120\right) x)^3}-\frac{6}{5 ( \left(31500120\right) x)^4}$
|
1/150
|
Numeric-One-8
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
881
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(328787282\right) x)+4) \csc ( \left(328787282\right) x)}{5 ( \left(328787282\right) x)^3}-\frac{6}{5 ( \left(328787282\right) x)^4}$
|
1/150
|
Numeric-One-9
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
882
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(9159041214\right) x)+4) \csc ( \left(9159041214\right) x)}{5 ( \left(9159041214\right) x)^3}-\frac{6}{5 ( \left(9159041214\right) x)^4}$
|
1/150
|
Numeric-One-10
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
883
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(2\right) x)+4) \csc ( \left(2\right) x)}{5 \left(3\right) ( \left(2\right) x)^3}-\frac{6}{5 \left(3\right) ( \left(2\right) x)^4}$
|
3**(-1)/150
|
Numeric-All-1
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
884
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(17\right) x)+4) \csc ( \left(17\right) x)}{5 \left(17\right) ( \left(17\right) x)^3}-\frac{6}{5 \left(17\right) ( \left(17\right) x)^4}$
|
17**(-1)/150
|
Numeric-All-2
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
885
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(240\right) x)+4) \csc ( \left(240\right) x)}{5 \left(436\right) ( \left(240\right) x)^3}-\frac{6}{5 \left(436\right) ( \left(240\right) x)^4}$
|
436**(-1)/150
|
Numeric-All-3
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
886
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(3983\right) x)+4) \csc ( \left(3983\right) x)}{5 \left(5264\right) ( \left(3983\right) x)^3}-\frac{6}{5 \left(5264\right) ( \left(3983\right) x)^4}$
|
5264**(-1)/150
|
Numeric-All-4
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
887
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(25076\right) x)+4) \csc ( \left(25076\right) x)}{5 \left(27299\right) ( \left(25076\right) x)^3}-\frac{6}{5 \left(27299\right) ( \left(25076\right) x)^4}$
|
27299**(-1)/150
|
Numeric-All-5
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
888
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(227448\right) x)+4) \csc ( \left(227448\right) x)}{5 \left(569235\right) ( \left(227448\right) x)^3}-\frac{6}{5 \left(569235\right) ( \left(227448\right) x)^4}$
|
569235**(-1)/150
|
Numeric-All-6
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
889
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(2793400\right) x)+4) \csc ( \left(2793400\right) x)}{5 \left(4949178\right) ( \left(2793400\right) x)^3}-\frac{6}{5 \left(4949178\right) ( \left(2793400\right) x)^4}$
|
4949178**(-1)/150
|
Numeric-All-7
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
890
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(68563430\right) x)+4) \csc ( \left(68563430\right) x)}{5 \left(34731312\right) ( \left(68563430\right) x)^3}-\frac{6}{5 \left(34731312\right) ( \left(68563430\right) x)^4}$
|
34731312**(-1)/150
|
Numeric-All-8
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
891
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(393062393\right) x)+4) \csc ( \left(393062393\right) x)}{5 \left(664679645\right) ( \left(393062393\right) x)^3}-\frac{6}{5 \left(664679645\right) ( \left(393062393\right) x)^4}$
|
664679645**(-1)/150
|
Numeric-All-9
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
892
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( \left(1761689734\right) x)+4) \csc ( \left(1761689734\right) x)}{5 \left(4161683371\right) ( \left(1761689734\right) x)^3}-\frac{6}{5 \left(4161683371\right) ( \left(1761689734\right) x)^4}$
|
4161683371**(-1)/150
|
Numeric-All-10
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
893
|
Compute $\lim_{x \to 0}\frac{(2 \cos (F x)+4) \csc (F x)}{5 (F x)^3}-\frac{6}{5 (F x)^4}$
|
1/150
|
Symbolic-1
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
894
|
Compute $\lim_{x \to 0}\frac{(2 \cos ( x)+4) \csc ( x)}{5 A ( x)^3}-\frac{6}{5 A ( x)^4}$
|
1/(150*A)
|
Symbolic-1
|
U-Math
sequences_series
068e40ce-9108-4ef8-8ee5-0d1471ebbe43
|
|
895
|
Evaluate
$ \lim_{x \to 0^+} \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) \left( \frac{ \tan\left( \frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x}{2} \right) }{ \frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x}{2} } \right)^{ \frac{ \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) 3}{( \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-All-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
896
|
Evaluate
$ \lim_{x \to 0^+} \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) \left( \frac{ \tan\left( \frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x}{2} \right) }{ \frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x}{2} } \right)^{ \frac{ \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) 3}{( \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-All-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
897
|
Evaluate
$ \lim_{x \to 0^+} \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) \left( \frac{ \tan\left( \frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x}{2} \right) }{ \frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x}{2} } \right)^{ \frac{ \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) 3}{( \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-All-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
898
|
Evaluate
$ \lim_{x \to 0^+} \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) \left( \frac{ \tan\left( \frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x}{2} \right) }{ \frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x}{2} } \right)^{ \frac{ \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) 3}{( \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-All-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
899
|
Evaluate
$ \lim_{x \to 0^+} \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) \left( \frac{ \tan\left( \frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x}{2} \right) }{ \frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x}{2} } \right)^{ \frac{ \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) 3}{( \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-All-Easy
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
|
900
|
Evaluate
$ \lim_{x \to 0^+} \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) \left( \frac{ \tan\left( \frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x}{2} \right) }{ \frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x}{2} } \right)^{ \frac{ \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) 3}{( \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x)^2} } $
|
e**(1/4)
|
Equivalence-All-Hard
|
U-Math
differential_calc
363dd580-f1fc-4867-a6ef-db2a03139745
|
Subsets and Splits
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