Question

Evaluate: $\lim_{x\to 0}\frac{\sin^3x-x^3\operatorname{sgn}\left(1-\left[\frac{x}{\sin^{-1}x}\right]\right)}{x\tan^2 x\sin(\pi\cos x)}$

score 1.3k · Answer 1 · 2018-05-30 20:42:13

1.3k

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Evaluate: $\lim_{x\to 0}\frac{\sin^3x-x^3\operatorname{sgn}\left(1-\left[\frac{x}{\sin^{-1}x}\right]\right)}{x\tan^2 x\sin(\pi\cos x)}$

Published on 30 May 2018 - 20:42

score 220 · Answer 2 · 2018-05-31 12:43:36

220

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Evaluate $ \displaystyle\lim_{x\to1} \frac{x^{\frac{1}{13}}-x^{\frac{1}{7}}}{x^{\frac{1}{5}}-x^{\frac{1}{3}}} $

Published on 31 May 2018 - 12:43

score 45 · Answer 3 · 2018-05-31 17:10:25

45

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Summation limit

Published on 31 May 2018 - 17:10

score 52 · Answer 4 · 2026-03-25 14:25:10

52

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if $g(x)=\lim_{n→∞}\frac{\{x\}^{2n}-1}{\{x\}^{2n}+1}$ where $\{x\}=$fractional part of $x$, then find g(x).

Published on 25 Mar 2026 - 14:25

score 77 · Answer 5 · 2018-06-01 09:43:35

77

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Evaluate $\,\lim_{n\to\infty}\frac{n^2}{({n^2+1^2})^{3/2}} + \frac{n^2}{({n^2+3^2})^{3/2}} + \cdots + \frac{n^2}{({n^2+(n-1)^2})^{3/2}}$

Published on 01 Jun 2018 - 9:43

score 1k · Answer 6 · 2018-06-02 13:40:00

1k

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Evaluate $\lim_{x\to \infty}\frac{x^{2018}+2017^x}{x^{2017}+2018^x}$

Published on 02 Jun 2018 - 13:40

score 118 · Answer 7 · 2018-06-02 17:00:21

118

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Find multivariable limit $\lim_{(x,y)\to(0,0)}\frac{x^2y^2}{\sqrt{x^2y^2+(x-y)^2}}$

Published on 02 Jun 2018 - 17:00

score 167 · Answer 8 · 2018-06-05 16:29:27

167

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Checking convergence of $\sum_{n=2}^{\infty} \frac{1}{(n\log(n))^p}$

Published on 05 Jun 2018 - 16:29

score 51 · Answer 9 · 2018-06-06 12:38:50

51

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Limit with denominator = $0$

Published on 06 Jun 2018 - 12:38

score 222 · Answer 10 · 2018-06-07 06:09:40

222

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Find $\lim_{n\to\infty}\int_0^{\frac {\pi}{3}}\frac {\sin^nx}{\sin^nx+\cos^nx}dx$

Published on 07 Jun 2018 - 6:09

score 99 · Answer 11 · 2018-06-09 20:07:35

99

Views

How do I find the limit without using L'Hopitals?

Published on 09 Jun 2018 - 20:07

score 35 · Answer 12 · 2018-06-10 08:04:24

35

Views

How to determine if $\sum \frac{(n-\ln(n))^n}{2^n \cdot n^n}$ converges?

Published on 10 Jun 2018 - 8:04

score 106 · Answer 13 · 2018-06-13 12:04:49

106

Views

Finding limit for infinite quantities.

Published on 13 Jun 2018 - 12:04

score 78 · Answer 14 · 2018-06-16 05:00:06

78

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Finding $\lim\limits_{n→∞}\frac{n^p \sin^2(n!)}{n+1}$

Published on 16 Jun 2018 - 5:00

score 98 · Answer 15 · 2018-06-16 05:29:32

98

Views

Find $\lim_{x \to \infty} (-1)^{x-1}\sin(\pi\sqrt{x^2+0.5x+1})$ with $x\in\mathbb{N}$

Published on 16 Jun 2018 - 5:29

List Question

Evaluate: $\lim_{x\to 0}\frac{\sin^3x-x^3\operatorname{sgn}\left(1-\left[\frac{x}{\sin^{-1}x}\right]\right)}{x\tan^2 x\sin(\pi\cos x)}$

Evaluate $ \displaystyle\lim_{x\to1} \frac{x^{\frac{1}{13}}-x^{\frac{1}{7}}}{x^{\frac{1}{5}}-x^{\frac{1}{3}}} $

Summation limit

if $g(x)=\lim_{n→∞}\frac{\{x\}^{2n}-1}{\{x\}^{2n}+1}$ where $\{x\}=$fractional part of $x$, then find g(x).

Evaluate $\,\lim_{n\to\infty}\frac{n^2}{({n^2+1^2})^{3/2}} + \frac{n^2}{({n^2+3^2})^{3/2}} + \cdots + \frac{n^2}{({n^2+(n-1)^2})^{3/2}}$

Evaluate $\lim_{x\to \infty}\frac{x^{2018}+2017^x}{x^{2017}+2018^x}$

Find multivariable limit $\lim_{(x,y)\to(0,0)}\frac{x^2y^2}{\sqrt{x^2y^2+(x-y)^2}}$

Checking convergence of $\sum_{n=2}^{\infty} \frac{1}{(n\log(n))^p}$

Limit with denominator = $0$

Find $\lim_{n\to\infty}\int_0^{\frac {\pi}{3}}\frac {\sin^nx}{\sin^nx+\cos^nx}dx$

How do I find the limit without using L'Hopitals?

How to determine if $\sum \frac{(n-\ln(n))^n}{2^n \cdot n^n}$ converges?

Finding limit for infinite quantities.

Finding $\lim\limits_{n→∞}\frac{n^p \sin^2(n!)}{n+1}$

Find $\lim_{x \to \infty} (-1)^{x-1}\sin(\pi\sqrt{x^2+0.5x+1})$ with $x\in\mathbb{N}$

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