Question

Does the following $\sin$-series converges?

score 75 · Answer 1 · 2026-04-11 01:09:53

75

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Does the following $\sin$-series converges?

Published on 11 Apr 2026 - 1:09

score 3.3k · Answer 2 · 2026-04-13 05:59:22

3.3k

Views

The function $f(x)=\tan^{-1}(x)$ is not uniformly continuous on $\Bbb{R}$

Published on 13 Apr 2026 - 5:59

score 50 · Answer 3 · 2026-04-15 12:35:52

50

Views

Defining $n$ for $\lim_{x\to \pm \infty}\frac{1}{x^{n}}=0$.

Published on 15 Apr 2026 - 12:35

score 75 · Answer 4 · 2026-04-15 08:20:34

75

Views

Find limit of $\lim_{x \to 0^+}\frac{\sin^2(x)}{e^{-1/x}}$

Published on 15 Apr 2026 - 8:20

score 183 · Answer 5 · 2026-04-16 14:54:59

183

Views

Limit of $\frac{\sqrt[n]{(n+1)(n+2)\cdots(2n)}}n$

Published on 16 Apr 2026 - 14:54

score 122 · Answer 6 · 2026-04-15 02:36:17

122

Views

Compute $\lim_{n\to\infty}3\frac {{n!}^{\frac 1n}}{n}.$

Published on 15 Apr 2026 - 2:36

score 86 · Answer 7 · 2026-04-14 07:09:47

86

Views

Relation between summing over an infinite but countable set of elements, limits, integrals

Published on 14 Apr 2026 - 7:09

score 2.4k · Answer 8 · 2026-04-15 19:56:12

2.4k

Views

Prove that $f(x)=\begin{cases}x& \text{if $x$ is rational},\\0 &\text{if $x$ is irrational}\end{cases}$ does not possess a derivative anywhere

Published on 15 Apr 2026 - 19:56

score 42 · Answer 9 · 2026-04-16 00:46:47

42

Views

For what conditions of $a$ and $b$, it follows that $ \lim_{x \to \infty} \frac{\ln^a x}{x^b}=0 $?

Published on 16 Apr 2026 - 0:46

score 147 · Answer 10 · 2026-04-16 03:33:43

147

Views

Find limit $\lim_{x \to 0}\frac{\arctan 3x}{\ln((1-x)^2)}$

Published on 16 Apr 2026 - 3:33

score 52 · Answer 11 · 2026-04-16 18:01:01

52

Views

$\lim_{x \to 0}\frac{2\mu(e^x(x^2-x+1)-1)-e^x(x^2-2x+2)+2}{x(2\mu(e^x(x-1)+1)-e^x(x-2)-2)}=\mu$

Published on 16 Apr 2026 - 18:01

score 68 · Answer 12 · 2026-04-09 19:06:46

68

Views

Limit of a function at a point, undefined?

Published on 09 Apr 2026 - 19:06

score 144 · Answer 13 · 2026-04-15 14:03:52

144

Views

Limit of a piecewise function

Published on 15 Apr 2026 - 14:03

score 83 · Answer 14 · 2026-04-23 17:04:06

83

Views

Show that $\lim_{x\to\infty}x^\frac{m}{m+1}(x^\frac{1}{m+1} - (x-1)^\frac{1}{m+1}) = \frac{1}{m+1}$ using the Mean Value Theorem

Published on 23 Apr 2026 - 17:04

score 1k · Answer 15 · 2026-04-14 06:42:58

1k

Views

Proving $\lim_{x\to\pi/2^-}\tan{x}=\infty$, using $\epsilon$-$\delta$

Published on 14 Apr 2026 - 6:42

List Question

Does the following $\sin$-series converges?

The function $f(x)=\tan^{-1}(x)$ is not uniformly continuous on $\Bbb{R}$

Defining $n$ for $\lim_{x\to \pm \infty}\frac{1}{x^{n}}=0$.

Find limit of $\lim_{x \to 0^+}\frac{\sin^2(x)}{e^{-1/x}}$

Limit of $\frac{\sqrt[n]{(n+1)(n+2)\cdots(2n)}}n$

Compute $\lim_{n\to\infty}3\frac {{n!}^{\frac 1n}}{n}.$

Relation between summing over an infinite but countable set of elements, limits, integrals

Prove that $f(x)=\begin{cases}x& \text{if $x$ is rational},\\0 &\text{if $x$ is irrational}\end{cases}$ does not possess a derivative anywhere

For what conditions of $a$ and $b$, it follows that $ \lim_{x \to \infty} \frac{\ln^a x}{x^b}=0 $?

Find limit $\lim_{x \to 0}\frac{\arctan 3x}{\ln((1-x)^2)}$

$\lim_{x \to 0}\frac{2\mu(e^x(x^2-x+1)-1)-e^x(x^2-2x+2)+2}{x(2\mu(e^x(x-1)+1)-e^x(x-2)-2)}=\mu$

Limit of a function at a point, undefined?

Limit of a piecewise function

Show that $\lim_{x\to\infty}x^\frac{m}{m+1}(x^\frac{1}{m+1} - (x-1)^\frac{1}{m+1}) = \frac{1}{m+1}$ using the Mean Value Theorem

Proving $\lim_{x\to\pi/2^-}\tan{x}=\infty$, using $\epsilon$-$\delta$

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