Question

An elementary proof for a series involving logarithm

score 627 · Answer 1 · 2026-04-25 08:53:03

627

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An elementary proof for a series involving logarithm

Published on 25 Apr 2026 - 8:53

score 80 · Answer 2 · 2026-04-16 19:55:20

80

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Differentiate $f(x)=\frac{\cos^{-1}\frac{x}{2}}{\sqrt{2x+7}}$, $-2<x<2$

Published on 16 Apr 2026 - 19:55

score 83 · Answer 3 · 2026-04-15 22:34:10

83

Views

Prove that $f$ has a limit at infinity, provided that $|f(x)-f(x_n)| \leq 1/n$

Published on 15 Apr 2026 - 22:34

score 1.6k · Answer 4 · 2026-04-15 11:45:15

1.6k

Views

Prove that there exists only one number $x \in \mathbb{R}$ such that $\sin(x)=x-1$.

Published on 15 Apr 2026 - 11:45

score 62 · Answer 5 · 2026-04-09 04:22:03

62

Views

Calculus about solving equation with exp.

Published on 09 Apr 2026 - 4:22

score 351 · Answer 6 · 2026-05-11 09:08:43

351

Views

Finding $\int\frac{1}{(1+\sin^2\theta)^{\frac{3}{2}}}d\theta$

Published on 11 May 2026 - 9:08

score 73 · Answer 7 · 2026-04-16 07:41:05

Can you get the function equations just based on the graph ( without knowing whether it is linear,quadratic...)

score 58 · Answer 8 · 2026-05-14 03:47:45

58

Views

Calculus involving Integrals

Published on 14 May 2026 - 3:47

score 101 · Answer 9 · 2026-04-16 03:24:53

101

Views

If $\{a_n\}$ are the Fibonacci numbers, then does $\sum_{n=0}^{\infty} \frac{1}{a_n}$ converge?

Published on 16 Apr 2026 - 3:24

score 41 · Answer 10 · 2026-05-15 14:11:05

41

Views

Continuity: difference between these terms and phrases

Published on 15 May 2026 - 14:11

score 151 · Answer 11 · 2026-04-09 08:11:58

151

Views

Understanding Cauchy Mean Value Theorem

Published on 09 Apr 2026 - 8:11

score 81 · Answer 12 · 2026-05-11 09:32:21

81

Views

Why does $y \int_0^\infty x^2 e^{-y|x|} \, dx=\frac 1 {y^2}\int_0^\infty x^2 e^{-x}\,dx$?

Published on 11 May 2026 - 9:32

score 114 · Answer 13 · 2026-04-18 03:24:57

114

Views

Show $\lim_{(x, y) \to (0, 0)} \frac{x^2 + y^2}{y}$ does not exist

Published on 18 Apr 2026 - 3:24

score 46 · Answer 14 · 2026-05-11 17:28:08

46

Views

Max and minimum height on the surface

Published on 11 May 2026 - 17:28

score 502 · Answer 15 · 2026-04-17 15:31:41

502

Views

How to evaluate $\int_0^1 \frac{1-x}{\ln x}(x+x^2+x^{2^2}+x^{2^3}+x^{2^4}+\ldots) \, dx$?

Published on 17 Apr 2026 - 15:31

List Question

An elementary proof for a series involving logarithm

Differentiate $f(x)=\frac{\cos^{-1}\frac{x}{2}}{\sqrt{2x+7}}$, $-2<x<2$

Prove that $f$ has a limit at infinity, provided that $|f(x)-f(x_n)| \leq 1/n$

Prove that there exists only one number $x \in \mathbb{R}$ such that $\sin(x)=x-1$.

Calculus about solving equation with exp.

Finding $\int\frac{1}{(1+\sin^2\theta)^{\frac{3}{2}}}d\theta$

Can you get the function equations just based on the graph ( without knowing whether it is linear,quadratic...)

Calculus involving Integrals

If $\{a_n\}$ are the Fibonacci numbers, then does $\sum_{n=0}^{\infty} \frac{1}{a_n}$ converge?

Continuity: difference between these terms and phrases

Understanding Cauchy Mean Value Theorem

Why does $y \int_0^\infty x^2 e^{-y|x|} \, dx=\frac 1 {y^2}\int_0^\infty x^2 e^{-x}\,dx$?

Show $\lim_{(x, y) \to (0, 0)} \frac{x^2 + y^2}{y}$ does not exist

Max and minimum height on the surface

How to evaluate $\int_0^1 \frac{1-x}{\ln x}(x+x^2+x^{2^2}+x^{2^3}+x^{2^4}+\ldots) \, dx$?

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