Index stringlengths 1 5 | Challenge stringlengths 41 1.59k | Answer in Latex stringclasses 198
values | Answer in Sympy stringlengths 1 783 | Variation stringclasses 33
values | Source stringclasses 100
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201 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) \cdot e^{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
202 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \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) \cdot e^{ \left(\frac{\sinh{\left(\log{\left(B x... | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
203 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) \cdot e^{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
204 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \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) \cdot e^{ \left(\frac{\log_B\left(\frac{x}{e}\ri... | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
205 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) \cdot e^{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
206 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \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) \cdot e^{ \left(\frac{B \sum_{N=1}^{\infty} \fra... | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
207 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) \cdot e^{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
208 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \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) \cdot e^{ \left(- \frac{2 i \left(e^{4 i B x} + ... | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
209 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) \cdot e^{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
210 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) \cdot e^{ \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\ri... | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
211 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) \cdot e^{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
212 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) \cdot e^{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
213 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) \cdot e^{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
214 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) \cdot e^{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
215 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) \cdot e^{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
216 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) \cdot e^{ \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 \righ... | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
217 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) \cdot e^{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
218 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) \cdot e^{ \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\rig... | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
219 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) \cdot e^{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
220 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) \cdot e^{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
221 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) \cdot e^{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
222 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) \cdot e^{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
223 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) \cdot e^{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
224 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) \cdot e^{ \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**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
225 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) \cdot e^{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
226 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) \cdot e^{ \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\righ... | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
227 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) \cdot e^{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
228 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) \cdot e^{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
229 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) \cdot e^{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
230 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) \cdot e^{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
231 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) \cdot e^{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
232 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) \cdot e^{ \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) \c... | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
233 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) \cdot e^{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
234 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \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) \cdot e^{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}... | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
235 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) \cdot e^{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
236 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \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) \cdot e^{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \ri... | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
237 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) \cdot e^{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
238 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \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) \cdot e^{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \... | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
239 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) \cdot e^{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
240 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \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) \cdot e^{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \c... | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-All-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
241 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) \cdot e^{1 \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-One-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
242 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \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) \cdot e^{1 \cdot \sin(x)} $.
Assume A and B are ... | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-One-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
243 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) \cdot e^{1 \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-One-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
244 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) \cdot e^{1 \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-One-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
245 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) \cdot e^{1 \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-One-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
246 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) \cdot e^{1 \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-One-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
247 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) \cdot e^{1 \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-One-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
248 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) \cdot e^{1 \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-One-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
249 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) \cdot e^{1 \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-One-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
250 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = \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) \cdot e^{1 \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-One-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
251 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 7 \cdot e^{1 \cdot \sin(x)} $.
| -x**5*7/15 - x**4*7/8 + x**2*7/2 + x*7 + 7 | Numeric-One-1 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
252 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 46 \cdot e^{1 \cdot \sin(x)} $.
| -x**5*46/15 - x**4*46/8 + x**2*46/2 + x*46 + 46 | Numeric-One-2 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
253 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 434 \cdot e^{1 \cdot \sin(x)} $.
| -x**5*434/15 - x**4*434/8 + x**2*434/2 + x*434 + 434 | Numeric-One-3 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
254 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 5552 \cdot e^{1 \cdot \sin(x)} $.
| -x**5*5552/15 - x**4*5552/8 + x**2*5552/2 + x*5552 + 5552 | Numeric-One-4 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
255 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 15499 \cdot e^{1 \cdot \sin(x)} $.
| -x**5*15499/15 - x**4*15499/8 + x**2*15499/2 + x*15499 + 15499 | Numeric-One-5 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
256 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 251135 \cdot e^{1 \cdot \sin(x)} $.
| -x**5*251135/15 - x**4*251135/8 + x**2*251135/2 + x*251135 + 251135 | Numeric-One-6 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
257 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 5294692 \cdot e^{1 \cdot \sin(x)} $.
| -x**5*5294692/15 - x**4*5294692/8 + x**2*5294692/2 + x*5294692 + 5294692 | Numeric-One-7 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
258 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 69618436 \cdot e^{1 \cdot \sin(x)} $.
| -x**5*69618436/15 - x**4*69618436/8 + x**2*69618436/2 + x*69618436 + 69618436 | Numeric-One-8 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
259 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 449306754 \cdot e^{1 \cdot \sin(x)} $.
| -x**5*449306754/15 - x**4*449306754/8 + x**2*449306754/2 + x*449306754 + 449306754 | Numeric-One-9 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
260 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 7736930350 \cdot e^{1 \cdot \sin(x)} $.
| -x**5*7736930350/15 - x**4*7736930350/8 + x**2*7736930350/2 + x*7736930350 + 7736930350 | Numeric-One-10 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
261 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 1 \cdot e^{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-One-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
262 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 1 \cdot e^{ \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) \cdot \sin(x)} $.
Assume A and B are ... | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-One-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
263 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 1 \cdot e^{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-One-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
264 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 1 \cdot e^{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-One-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
265 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 1 \cdot e^{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-One-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
266 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 1 \cdot e^{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-One-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
267 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 1 \cdot e^{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-One-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
268 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 1 \cdot e^{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-One-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
269 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 1 \cdot e^{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-One-Easy | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
270 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 1 \cdot e^{ \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) \cdot \sin(x)} $.
Assume A and B are real and positive. | -x**5/15 - x**4/8 + x**2/2 + x + 1 | Equivalence-One-Hard | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
271 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 1 \cdot e^{4 \cdot \sin(x)} $.
| x**5*(4 - 10*4**3 + 4**5)/120 + x**4*(-4*4**2 + 4**4)/24 + x**3*(-4 + 4**3)/6 + x**2*4**2/2 + x*4 + 1 | Numeric-One-1 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
272 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 1 \cdot e^{12 \cdot \sin(x)} $.
| x**5*(12 - 10*12**3 + 12**5)/120 + x**4*(-4*12**2 + 12**4)/24 + x**3*(-12 + 12**3)/6 + x**2*12**2/2 + x*12 + 1 | Numeric-One-2 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
273 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 1 \cdot e^{788 \cdot \sin(x)} $.
| x**5*(788 - 10*788**3 + 788**5)/120 + x**4*(-4*788**2 + 788**4)/24 + x**3*(-788 + 788**3)/6 + x**2*788**2/2 + x*788 + 1 | Numeric-One-3 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
274 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 1 \cdot e^{1600 \cdot \sin(x)} $.
| x**5*(1600 - 10*1600**3 + 1600**5)/120 + x**4*(-4*1600**2 + 1600**4)/24 + x**3*(-1600 + 1600**3)/6 + x**2*1600**2/2 + x*1600 + 1 | Numeric-One-4 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
275 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 1 \cdot e^{16346 \cdot \sin(x)} $.
| x**5*(16346 - 10*16346**3 + 16346**5)/120 + x**4*(-4*16346**2 + 16346**4)/24 + x**3*(-16346 + 16346**3)/6 + x**2*16346**2/2 + x*16346 + 1 | Numeric-One-5 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
276 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 1 \cdot e^{959110 \cdot \sin(x)} $.
| x**5*(959110 - 10*959110**3 + 959110**5)/120 + x**4*(-4*959110**2 + 959110**4)/24 + x**3*(-959110 + 959110**3)/6 + x**2*959110**2/2 + x*959110 + 1 | Numeric-One-6 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
277 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 1 \cdot e^{9473540 \cdot \sin(x)} $.
| x**5*(9473540 - 10*9473540**3 + 9473540**5)/120 + x**4*(-4*9473540**2 + 9473540**4)/24 + x**3*(-9473540 + 9473540**3)/6 + x**2*9473540**2/2 + x*9473540 + 1 | Numeric-One-7 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
278 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 1 \cdot e^{57062853 \cdot \sin(x)} $.
| x**5*(57062853 - 10*57062853**3 + 57062853**5)/120 + x**4*(-4*57062853**2 + 57062853**4)/24 + x**3*(-57062853 + 57062853**3)/6 + x**2*57062853**2/2 + x*57062853 + 1 | Numeric-One-8 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
279 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 1 \cdot e^{850708129 \cdot \sin(x)} $.
| x**5*(850708129 - 10*850708129**3 + 850708129**5)/120 + x**4*(-4*850708129**2 + 850708129**4)/24 + x**3*(-850708129 + 850708129**3)/6 + x**2*850708129**2/2 + x*850708129 + 1 | Numeric-One-9 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
280 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 1 \cdot e^{5742768938 \cdot \sin(x)} $.
| x**5*(5742768938 - 10*5742768938**3 + 5742768938**5)/120 + x**4*(-4*5742768938**2 + 5742768938**4)/24 + x**3*(-5742768938 + 5742768938**3)/6 + x**2*5742768938**2/2 + x*5742768938 + 1 | Numeric-One-10 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
281 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 9 \cdot e^{8 \cdot \sin(x)} $.
| x**5*(8 - 10*8**3 + 8**5)*9/120 + x**4*(-4*8**2 + 8**4)*9/24 + x**3*(-8 + 8**3)*9/6 + x**2*8**2*9/2 + x*8*9 + 9 | Numeric-All-1 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
282 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 85 \cdot e^{79 \cdot \sin(x)} $.
| x**5*(79 - 10*79**3 + 79**5)*85/120 + x**4*(-4*79**2 + 79**4)*85/24 + x**3*(-79 + 79**3)*85/6 + x**2*79**2*85/2 + x*79*85 + 85 | Numeric-All-2 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
283 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 260 \cdot e^{815 \cdot \sin(x)} $.
| x**5*(815 - 10*815**3 + 815**5)*260/120 + x**4*(-4*815**2 + 815**4)*260/24 + x**3*(-815 + 815**3)*260/6 + x**2*815**2*260/2 + x*815*260 + 260 | Numeric-All-3 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
284 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 6779 \cdot e^{8979 \cdot \sin(x)} $.
| x**5*(8979 - 10*8979**3 + 8979**5)*6779/120 + x**4*(-4*8979**2 + 8979**4)*6779/24 + x**3*(-8979 + 8979**3)*6779/6 + x**2*8979**2*6779/2 + x*8979*6779 + 6779 | Numeric-All-4 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
285 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 54860 \cdot e^{15193 \cdot \sin(x)} $.
| x**5*(15193 - 10*15193**3 + 15193**5)*54860/120 + x**4*(-4*15193**2 + 15193**4)*54860/24 + x**3*(-15193 + 15193**3)*54860/6 + x**2*15193**2*54860/2 + x*15193*54860 + 54860 | Numeric-All-5 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
286 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 295579 \cdot e^{727633 \cdot \sin(x)} $.
| x**5*(727633 - 10*727633**3 + 727633**5)*295579/120 + x**4*(-4*727633**2 + 727633**4)*295579/24 + x**3*(-727633 + 727633**3)*295579/6 + x**2*727633**2*295579/2 + x*727633*295579 + 295579 | Numeric-All-6 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
287 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 6330676 \cdot e^{6690057 \cdot \sin(x)} $.
| x**5*(6690057 - 10*6690057**3 + 6690057**5)*6330676/120 + x**4*(-4*6690057**2 + 6690057**4)*6330676/24 + x**3*(-6690057 + 6690057**3)*6330676/6 + x**2*6690057**2*6330676/2 + x*6690057*6330676 + 6330676 | Numeric-All-7 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
288 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 94523787 \cdot e^{53507464 \cdot \sin(x)} $.
| x**5*(53507464 - 10*53507464**3 + 53507464**5)*94523787/120 + x**4*(-4*53507464**2 + 53507464**4)*94523787/24 + x**3*(-53507464 + 53507464**3)*94523787/6 + x**2*53507464**2*94523787/2 + x*53507464*94523787 + 94523787 | Numeric-All-8 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
289 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 610591507 \cdot e^{171843191 \cdot \sin(x)} $.
| x**5*(171843191 - 10*171843191**3 + 171843191**5)*610591507/120 + x**4*(-4*171843191**2 + 171843191**4)*610591507/24 + x**3*(-171843191 + 171843191**3)*610591507/6 + x**2*171843191**2*610591507/2 + x*171843191*610591507 + 610591507 | Numeric-All-9 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
290 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 5849491966 \cdot e^{4370479358 \cdot \sin(x)} $.
| x**5*(4370479358 - 10*4370479358**3 + 4370479358**5)*5849491966/120 + x**4*(-4*4370479358**2 + 4370479358**4)*5849491966/24 + x**3*(-4370479358 + 4370479358**3)*5849491966/6 + x**2*4370479358**2*5849491966/2 + x*4370479358*5849491966 + 5849491966 | Numeric-All-10 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
291 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = 1 \cdot e^{B \cdot \sin(x)} $.
Assume A and B are real and positive. | B**2*x**2/2 + B*x + x**5*(B**5 - 10*B**3 + B)/120 + x**4*(B**4 - 4*B**2)/24 + x**3*(B**3 - B)/6 + 1 | Symbolic-1 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
292 | Compute up to degree 5 ($x^5$) the terms of the Maclaurin series of $ f(x) = A \cdot e^{1 \cdot \sin(x)} $.
Assume A and B are real and positive. | -A*x**5/15 - A*x**4/8 + A*x**2/2 + A*x + A | Symbolic-1 | U-Math
sequences_series
1ccc052c-9604-4459-a752-98ebdf3e0764 | Series | |
293 | Find the radius of convergence of the following series. Assume A,B,G,H are real and positive.
$ \sum_{n=1}^\infty \frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \cdot (2 \cdot n)! \cdot ( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) \cdot x)^n}{ \left(\f... | exp(2)/4 | Equivalence-All-Easy | U-Math
sequences_series
ca5ffe7c-f495-43dc-a653-de477cabc185 | Series | |
294 | Find the radius of convergence of the following series. Assume A,B,G,H are real and positive.
$ \sum_{n=1}^\infty \frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \cdot (2 \cdot n)! \cdot ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)... | exp(2)/4 | Equivalence-All-Hard | U-Math
sequences_series
ca5ffe7c-f495-43dc-a653-de477cabc185 | Series | |
295 | Find the radius of convergence of the following series. Assume A,B,G,H are real and positive.
$ \sum_{n=1}^\infty \frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \cdot (2 \cdot n)! \cdot ( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) \cdot x)^n}{ \left(\f... | exp(2)/4 | Equivalence-All-Easy | U-Math
sequences_series
ca5ffe7c-f495-43dc-a653-de477cabc185 | Series | |
296 | Find the radius of convergence of the following series. Assume A,B,G,H are real and positive.
$ \sum_{n=1}^\infty \frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \cdot (2 \cdot n)! \cdot ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)... | exp(2)/4 | Equivalence-All-Hard | U-Math
sequences_series
ca5ffe7c-f495-43dc-a653-de477cabc185 | Series | |
297 | Find the radius of convergence of the following series. Assume A,B,G,H are real and positive.
$ \sum_{n=1}^\infty \frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \cdot (2 \cdot n)! \cdot ( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) \cdot x)^n}{ \left(\f... | exp(2)/4 | Equivalence-All-Easy | U-Math
sequences_series
ca5ffe7c-f495-43dc-a653-de477cabc185 | Series | |
298 | Find the radius of convergence of the following series. Assume A,B,G,H are real and positive.
$ \sum_{n=1}^\infty \frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \cdot (2 \cdot n)! \cdot ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)... | exp(2)/4 | Equivalence-All-Hard | U-Math
sequences_series
ca5ffe7c-f495-43dc-a653-de477cabc185 | Series | |
299 | Find the radius of convergence of the following series. Assume A,B,G,H are real and positive.
$ \sum_{n=1}^\infty \frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \cdot (2 \cdot n)! \cdot ( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) \cdot x)^n}{ \left(\f... | exp(2)/4 | Equivalence-All-Easy | U-Math
sequences_series
ca5ffe7c-f495-43dc-a653-de477cabc185 | Series | |
300 | Find the radius of convergence of the following series. Assume A,B,G,H are real and positive.
$ \sum_{n=1}^\infty \frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \cdot (2 \cdot n)! \cdot ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)... | exp(2)/4 | Equivalence-All-Hard | U-Math
sequences_series
ca5ffe7c-f495-43dc-a653-de477cabc185 | Series |
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