Question

Reasoning with integrals of exponential functions

score 77 · Answer 1 · 2020-07-21 01:54:15

77

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Reasoning with integrals of exponential functions

Published on 21 Jul 2020 - 1:54

score 87 · Answer 2 · 2020-07-21 01:57:32

87

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Convergence involving sub-exponential functions

Published on 21 Jul 2020 - 1:57

score 221 · Answer 3 · 2026-03-26 18:30:00

221

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How can I solve for the Jacobian matrix of a complementary log function?

Published on 26 Mar 2026 - 18:30

score 58 · Answer 4 · 2026-04-05 17:18:19

58

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Find $\int_0^{\frac{\pi}{2}} e^{-a(\sin(x)+\cos(x))} \, dx$ and/or $\int_0^{\frac{\pi}{2}} e^{-a(\sin(x)+\cos(x))} \sin(\cos(x)) \, dx$

Published on 05 Apr 2026 - 17:18

score 174 · Answer 5 · 2020-07-22 23:03:24

174

Views

Solving $ 2(2^x- 1) x^2 + (2^{x^2}-2)x = 2^{x+1} -2$

Published on 22 Jul 2020 - 23:03

score 101 · Answer 6 · 2026-03-30 14:43:54

101

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Prove that $\frac{d^n}{dx^n}(1-e^x)^n\Big\rvert_{x=0}=(-1)^nn!$

Published on 30 Mar 2026 - 14:43

score 953 · Answer 7 · 2026-04-02 22:42:47

953

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How to prove that $(a^m)^n=a^{mn}$ where $a,m,n$ are real numbers and a>0?

Published on 02 Apr 2026 - 22:42

score 94 · Answer 8 · 2020-07-24 08:37:42

94

Views

Integral with exponent and trigonometric functions

Published on 24 Jul 2020 - 8:37

score 229 · Answer 9 · 2020-07-25 07:45:47

229

Views

Let $f(x)=\lim_{n\to \infty} (1-\sin x + e^{\frac 1n} \sin x)^n)$. If ....

Published on 25 Jul 2020 - 7:45

score 75 · Answer 10 · 2026-03-28 17:41:54

75

Views

Prove the inequality $u^{\alpha}v^{1-\alpha} \leq \alpha u + (1-\alpha)v $

Published on 28 Mar 2026 - 17:41

score 48 · Answer 11 · 2026-04-09 11:07:27

48

Views

Computation of a mean

Published on 09 Apr 2026 - 11:07

score 49 · Answer 12 · 2026-04-07 01:42:17

49

Views

For which $p$ do the following functions converge in $L^p([0,\infty),leb)$?

Published on 07 Apr 2026 - 1:42

score 148 · Answer 13 · 2020-07-28 21:38:00

148

Views

Are real numbers enough to solve simpler exponential equations such as $2^x=5$, $(1/e)^x=3$, and $\pi^x=e$?

Published on 28 Jul 2020 - 21:38

score 123 · Answer 14 · 2020-07-29 01:58:23

123

Views

Differentiating powers of e where the power is an exponential function like $e^{a^x}$ when $a$ is a constant

Published on 29 Jul 2020 - 1:58

score 133 · Answer 15 · 2020-07-30 10:34:24

133

Views

Find $\lim _{x \to \infty}\frac{5^x+7^{x+1}}{7^x+5^{x+1}}$

Published on 30 Jul 2020 - 10:34

List Question

Reasoning with integrals of exponential functions

Convergence involving sub-exponential functions

How can I solve for the Jacobian matrix of a complementary log function?

Find $\int_0^{\frac{\pi}{2}} e^{-a(\sin(x)+\cos(x))} \, dx$ and/or $\int_0^{\frac{\pi}{2}} e^{-a(\sin(x)+\cos(x))} \sin(\cos(x)) \, dx$

Solving $ 2(2^x- 1) x^2 + (2^{x^2}-2)x = 2^{x+1} -2$

Prove that $\frac{d^n}{dx^n}(1-e^x)^n\Big\rvert_{x=0}=(-1)^nn!$

How to prove that $(a^m)^n=a^{mn}$ where $a,m,n$ are real numbers and a>0?

Integral with exponent and trigonometric functions

Let $f(x)=\lim_{n\to \infty} (1-\sin x + e^{\frac 1n} \sin x)^n)$. If ....

Prove the inequality $u^{\alpha}v^{1-\alpha} \leq \alpha u + (1-\alpha)v $

Computation of a mean

For which $p$ do the following functions converge in $L^p([0,\infty),leb)$?

Are real numbers enough to solve simpler exponential equations such as $2^x=5$, $(1/e)^x=3$, and $\pi^x=e$?

Differentiating powers of e where the power is an exponential function like $e^{a^x}$ when $a$ is a constant

Find $\lim _{x \to \infty}\frac{5^x+7^{x+1}}{7^x+5^{x+1}}$

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