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
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|---|---|---|---|---|---|
1101
|
Evaluate
$ \lim_{x \to \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x }{ x - 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1102
|
Evaluate
$ \lim_{x \to \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) 5} \left( \frac{ 3 \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x }{ 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) }-\frac{ 3 \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) }{ \ln\left(\frac{ 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) }\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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1103
|
Evaluate
$ \lim_{x \to \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x }{ x - 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) }{ \ln\left(\frac{ x }{ 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1104
|
Evaluate
$ \lim_{x \to \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) 5} \left( \frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x }{ 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) }-\frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) }{ \ln\left(\frac{ 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) }\right) } \right)^{ \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1105
|
Evaluate
$ \lim_{x \to \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x }{ x - 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) }{ \ln\left(\frac{ x }{ 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1106
|
Evaluate
$ \lim_{x \to \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) 5} \left( \frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x }{ 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) }-\frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) }{ \ln\left(\frac{ 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) }\right) } \right)^{ \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1107
|
Evaluate
$ \lim_{x \to \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x }{ x - 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) }{ \ln\left(\frac{ x }{ 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1108
|
Evaluate
$ \lim_{x \to \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) 5} \left( \frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x }{ 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) }-\frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) }{ \ln\left(\frac{ 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) }\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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1109
|
Evaluate
$ \lim_{x \to \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) x }{ x - 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) }{ \ln\left(\frac{ x }{ 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1110
|
Evaluate
$ \lim_{x \to \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) 5} \left( \frac{ 3 \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) x }{ x - 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) }-\frac{ 3 \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) }{ \ln\left(\frac{ 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) }\right) } \right)^{ \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1111
|
Evaluate
$ \lim_{x \to \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) x }{ x - 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) }{ \ln\left(\frac{ x }{ 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1112
|
Evaluate
$ \lim_{x \to \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) 5} \left( \frac{ 3 \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) x }{ x - 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) }-\frac{ 3 \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) }{ \ln\left(\frac{ 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) }\right) } \right)^{ \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1113
|
Evaluate
$ \lim_{x \to \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) x }{ x - 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) }{ \ln\left(\frac{ x }{ 5 \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1114
|
Evaluate
$ \lim_{x \to \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) 5} \left( \frac{ 3 \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) x }{ x - 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) }-\frac{ 3 \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) }{ \ln\left(\frac{ 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) }\right) } \right)^{ \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1115
|
Evaluate
$ \lim_{x \to \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) x }{ x - 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1116
|
Evaluate
$ \lim_{x \to \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) 5} \left( \frac{ 3 \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) x }{ x - 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) }-\frac{ 3 \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) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) }\right) } \right)^{ \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1117
|
Evaluate
$ \lim_{x \to \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) x }{ x - 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1118
|
Evaluate
$ \lim_{x \to \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) 5} \left( \frac{ 3 \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) x }{ x - 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) }-\frac{ 3 \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) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) }\right) } \right)^{ \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1119
|
Evaluate
$ \lim_{x \to \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) x }{ x - 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1120
|
Evaluate
$ \lim_{x \to \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) 5} \left( \frac{ 3 \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) x }{ x - 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) }-\frac{ 3 \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) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) }\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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1121
|
Evaluate
$ \lim_{x \to \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x }{ x - 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) }{ \ln\left(\frac{ x }{ 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1122
|
Evaluate
$ \lim_{x \to \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) 5} \left( \frac{ 3 \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x }{ x - 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) }-\frac{ 3 \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1123
|
Evaluate
$ \lim_{x \to \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x }{ x - 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) }{ \ln\left(\frac{ x }{ 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1124
|
Evaluate
$ \lim_{x \to \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) 5} \left( \frac{ 3 \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x }{ x - 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) }-\frac{ 3 \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) }\right) } \right)^{ \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1125
|
Evaluate
$ \lim_{x \to \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x }{ x - 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) }{ \ln\left(\frac{ x }{ 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1126
|
Evaluate
$ \lim_{x \to \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) 5} \left( \frac{ 3 \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x }{ x - 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) }-\frac{ 3 \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) }\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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1127
|
Evaluate
$ \lim_{x \to \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x }{ x - 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) }{ \ln\left(\frac{ x }{ 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1128
|
Evaluate
$ \lim_{x \to \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) 5} \left( \frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x }{ x - 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) }-\frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1129
|
Evaluate
$ \lim_{x \to \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x }{ x - 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) }{ \ln\left(\frac{ x }{ 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1130
|
Evaluate
$ \lim_{x \to \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) 5} \left( \frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x }{ x - 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) }-\frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) }\right) } \right)^{ \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1131
|
Evaluate
$ \lim_{x \to \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x }{ x - 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) }{ \ln\left(\frac{ x }{ 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1132
|
Evaluate
$ \lim_{x \to \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) 5} \left( \frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x }{ x - 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) }-\frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) }\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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1133
|
Evaluate
$ \lim_{x \to \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) x }{ x - 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) }{ \ln\left(\frac{ x }{ 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1134
|
Evaluate
$ \lim_{x \to \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) 5} \left( \frac{ 3 \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) x }{ x - 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) }-\frac{ 3 \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) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1135
|
Evaluate
$ \lim_{x \to \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) x }{ x - 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) }{ \ln\left(\frac{ x }{ 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1136
|
Evaluate
$ \lim_{x \to \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) 5} \left( \frac{ 3 \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) x }{ x - 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) }-\frac{ 3 \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) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) }\right) } \right)^{ \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1137
|
Evaluate
$ \lim_{x \to \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) 5} \left( \frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) x }{ x - 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }-\frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) }{ \ln\left(\frac{ x }{ 5 \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) }\right) } \right)^{ \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1138
|
Evaluate
$ \lim_{x \to \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) 5} \left( \frac{ 3 \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) x }{ x - 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) }-\frac{ 3 \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) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) }\right) } \right)^{ \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1139
|
Evaluate
$ \lim_{x \to \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) 5} \left( \frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) x }{ x - 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }-\frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }\right) } \right)^{ \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1140
|
Evaluate
$ \lim_{x \to \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) 5} \left( \frac{ 3 \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) x }{ x - 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) }-\frac{ 3 \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) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) }\right) } \right)^{ \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1141
|
Evaluate
$ \lim_{x \to \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) 5} \left( \frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) x }{ x - 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }-\frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }\right) } \right)^{ \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1142
|
Evaluate
$ \lim_{x \to \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) 5} \left( \frac{ 3 \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) x }{ x - 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) }-\frac{ 3 \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) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) }\right) } \right)^{ \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1143
|
Evaluate
$ \lim_{x \to \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) 5} \left( \frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) x }{ x - 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }-\frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }\right) } \right)^{ \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1144
|
Evaluate
$ \lim_{x \to \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) 5} \left( \frac{ 3 \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) x }{ x - 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) }-\frac{ 3 \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) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) }\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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1145
|
Evaluate
$ \lim_{x \to \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) 5} \left( \frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x }{ x - 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }-\frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }\right) } \right)^{ \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1146
|
Evaluate
$ \lim_{x \to \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) 5} \left( \frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x }{ x - 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) }-\frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1147
|
Evaluate
$ \lim_{x \to \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) 5} \left( \frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x }{ x - 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }-\frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }\right) } \right)^{ \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1148
|
Evaluate
$ \lim_{x \to \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) 5} \left( \frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x }{ x - 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) }-\frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) }\right) } \right)^{ \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1149
|
Evaluate
$ \lim_{x \to \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) 5} \left( \frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x }{ x - 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }-\frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }\right) } \right)^{ \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1150
|
Evaluate
$ \lim_{x \to \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) 5} \left( \frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x }{ x - 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) }-\frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) }\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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1151
|
Evaluate
$ \lim_{x \to \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) 5} \left( \frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x }{ x - 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }-\frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }\right) } \right)^{ \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1152
|
Evaluate
$ \lim_{x \to \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) 5} \left( \frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x }{ x - 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) }-\frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1153
|
Evaluate
$ \lim_{x \to \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) 5} \left( \frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x }{ x - 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }-\frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }\right) } \right)^{ \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1154
|
Evaluate
$ \lim_{x \to \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) 5} \left( \frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x }{ x - 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) }-\frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) }\right) } \right)^{ \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1155
|
Evaluate
$ \lim_{x \to \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) 5} \left( \frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) x }{ x - 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }-\frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }\right) } \right)^{ \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1156
|
Evaluate
$ \lim_{x \to \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) 5} \left( \frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) x }{ x - 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) }-\frac{ 3 \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) }\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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1157
|
Evaluate
$ \lim_{x \to \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) 5} \left( \frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) x }{ x - 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }-\frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }\right) } \right)^{ \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1158
|
Evaluate
$ \lim_{x \to \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) 5} \left( \frac{ 3 \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) x }{ x - 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) }-\frac{ 3 \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) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1159
|
Evaluate
$ \lim_{x \to \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) 5} \left( \frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) x }{ x - 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }-\frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }\right) } \right)^{ \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1160
|
Evaluate
$ \lim_{x \to \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) 5} \left( \frac{ 3 \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) x }{ x - 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) }-\frac{ 3 \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) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) }\right) } \right)^{ \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1161
|
Evaluate
$ \lim_{x \to \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) 5} \left( \frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) x }{ x - 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }-\frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) }\right) } \right)^{ \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1162
|
Evaluate
$ \lim_{x \to \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) 5} \left( \frac{ 3 \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) x }{ x - 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) }-\frac{ 3 \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) }{ \ln\left(\frac{ x }{ 5 \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) }\right) } \right)^{ \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1163
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) 5} \left( \frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }-\frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }\right) } \right)^{ \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1164
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) 5} \left( \frac{ 3 \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) }-\frac{ 3 \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) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) }\right) } \right)^{ \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1165
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) 5} \left( \frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }-\frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }\right) } \right)^{ \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1166
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) 5} \left( \frac{ 3 \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) }-\frac{ 3 \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) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) }\right) } \right)^{ \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1167
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) 5} \left( \frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }-\frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }\right) } \right)^{ \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1168
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) 5} \left( \frac{ 3 \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) }-\frac{ 3 \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) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) }\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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1169
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) 5} \left( \frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }-\frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }\right) } \right)^{ \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1170
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) 5} \left( \frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) }-\frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} 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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1171
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) 5} \left( \frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }-\frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }\right) } \right)^{ \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1172
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) 5} \left( \frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) }-\frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) }\right) } \right)^{ \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1173
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) 5} \left( \frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }-\frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }\right) } \right)^{ \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1174
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) 5} \left( \frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) }-\frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) }\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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1175
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) 5} \left( \frac{ 3 \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }-\frac{ 3 \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }\right) } \right)^{ \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1176
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) 5} \left( \frac{ 3 \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) }-\frac{ 3 \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} 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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1177
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) 5} \left( \frac{ 3 \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }-\frac{ 3 \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }\right) } \right)^{ \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1178
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) 5} \left( \frac{ 3 \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) }-\frac{ 3 \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) }\right) } \right)^{ \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1179
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) 5} \left( \frac{ 3 \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }-\frac{ 3 \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }\right) } \right)^{ \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1180
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) 5} \left( \frac{ 3 \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) }-\frac{ 3 \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) }\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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1181
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) 5} \left( \frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }-\frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }\right) } \right)^{ \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1182
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) 5} \left( \frac{ 3 \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) }-\frac{ 3 \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) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} 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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1183
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) 5} \left( \frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }-\frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }\right) } \right)^{ \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1184
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) 5} \left( \frac{ 3 \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) }-\frac{ 3 \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) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) }\right) } \right)^{ \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1185
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) 5} \left( \frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }-\frac{ 3 \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) }\right) } \right)^{ \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1186
|
Evaluate
$ \lim_{x \to \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) 5} \left( \frac{ 3 \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) x }{ x - 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) }-\frac{ 3 \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) }{ \ln\left(\frac{ x }{ 5 \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) }\right) } \right)^{ \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1187
|
Evaluate
$ \lim_{x \to \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) 5} \left( \frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) x }{ x - 5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) }-\frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) }\right) } \right)^{ \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1188
|
Evaluate
$ \lim_{x \to \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) 5} \left( \frac{ 3 \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) x }{ x - 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) }-\frac{ 3 \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) }{ \ln\left(\frac{ 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) }\right) } \right)^{ \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1189
|
Evaluate
$ \lim_{x \to \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) 5} \left( \frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) x }{ x - 5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) }-\frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) }\right) } \right)^{ \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1190
|
Evaluate
$ \lim_{x \to \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) 5} \left( \frac{ 3 \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) x }{ x - 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) }-\frac{ 3 \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) }{ \ln\left(\frac{ 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) }\right) } \right)^{ \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1191
|
Evaluate
$ \lim_{x \to \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) 5} \left( \frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) x }{ x - 5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) }-\frac{ 3 \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) }\right) } \right)^{ \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1192
|
Evaluate
$ \lim_{x \to \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) 5} \left( \frac{ 3 \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) x }{ x - 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) }-\frac{ 3 \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) }{ \ln\left(\frac{ 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) }\right) } \right)^{ \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1193
|
Evaluate
$ \lim_{x \to \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) 5} \left( \frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x }{ x - 5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) }-\frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) }\right) } \right)^{ \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1194
|
Evaluate
$ \lim_{x \to \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) 5} \left( \frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x }{ 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) }-\frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) }{ \ln\left(\frac{ 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) }\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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1195
|
Evaluate
$ \lim_{x \to \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) 5} \left( \frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x }{ x - 5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) }-\frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) }\right) } \right)^{ \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1196
|
Evaluate
$ \lim_{x \to \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) 5} \left( \frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x }{ 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) }-\frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) }{ \ln\left(\frac{ 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) }\right) } \right)^{ \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1197
|
Evaluate
$ \lim_{x \to \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) 5} \left( \frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) x }{ x - 5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) }-\frac{ 3 \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) }{ \ln\left(\frac{ x }{ 5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) }\right) } \right)^{ \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1198
|
Evaluate
$ \lim_{x \to \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) 5} \left( \frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) x }{ 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) }-\frac{ 3 \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) }{ \ln\left(\frac{ 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) }\right) } \right)^{ \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1199
|
Evaluate
$ \lim_{x \to \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) 5} \left( \frac{ 3 \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) x }{ x - 5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) }-\frac{ 3 \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) }{ \ln\left(\frac{ x }{ 5 \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) }\right) } \right)^{ \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) } $
|
3/2
|
Equivalence-All-Easy
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
|
1200
|
Evaluate
$ \lim_{x \to \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) 5} \left( \frac{ 3 \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) x }{ 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) }-\frac{ 3 \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) }{ \ln\left(\frac{ 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) }\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) } $
|
3/2
|
Equivalence-All-Hard
|
U-Math
differential_calc
2d799998-115a-489b-a48b-57090954303e
|
Subsets and Splits
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