Question

How do I solve $\lim \limits_{x \to \frac{π}{3}} \frac{2 \sin x - \sqrt{3}}{\cos \frac{3x}{2}}$

score 205 · Answer 1 · 2018-12-23 19:23:40

205

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How do I solve $\lim \limits_{x \to \frac{π}{3}} \frac{2 \sin x - \sqrt{3}}{\cos \frac{3x}{2}}$

Published on 23 Dec 2018 - 19:23

score 689 · Answer 2 · 2018-12-23 20:41:24

689

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without L'Hospital's rule find the $\lim_{x\to 0+} (\csc x)^{\sin^2 x}$

Published on 23 Dec 2018 - 20:41

score 418 · Answer 3 · 2018-12-24 14:20:39

418

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Prove: $\lim\limits_{x\to\infty}\left(\sin^2\left(\frac{1}{x}\right)+\cos\frac1x\right)^{x^{2}}=\sqrt{e}$

Published on 24 Dec 2018 - 14:20

score 98 · Answer 4 · 2018-12-24 17:08:46

98

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Trouble with a sequence limit

Published on 24 Dec 2018 - 17:08

score 89 · Answer 5 · 2018-12-24 18:38:23

89

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How to calculate $ \lim_{x\to 0} (\frac{(5x + 1)^{20} - (20x + 1)^{5}}{\sqrt[5]{1 + 20x^{2}}-1}) $ without the rule of L'Hôpital?

Published on 24 Dec 2018 - 18:38

score 227 · Answer 6 · 2018-12-27 13:04:27

227

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Why L'Hospital Rule cannot apply in calculating $\lim_{x\rightarrow \infty}{(\cos {\frac{1}{x}} + \sin {\frac{1}{x^2}})^{\frac{1}{x^2}}}$

Published on 27 Dec 2018 - 13:04

score 88 · Answer 7 · 2018-12-28 19:14:08

88

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How to compute $\lim \limits_{x\to \infty} ((2x^3-2x^2+x)e^{1/x}-\sqrt{x^6+3})$ through Taylor series

Published on 28 Dec 2018 - 19:14

score 44 · Answer 8 · 2018-12-29 20:00:52

44

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How can I evaluate the left limit of this function?

Published on 29 Dec 2018 - 20:00

score 111 · Answer 9 · 2026-03-26 11:04:19

111

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Calculating $\lim\limits_{j \to \infty} \frac{j^{j/2}}{j!}$

Published on 26 Mar 2026 - 11:04

score 113 · Answer 10 · 2019-01-01 22:23:10

113

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How to find trigonometric limit $ \lim_{x\to π} \frac{\sin x}{x^2 - π^2} $

Published on 01 Jan 2019 - 22:23

score 179 · Answer 11 · 2019-01-02 12:39:36

179

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Show that if $\lim_{n \to \infty} x_n = 0$ if follows that $\lim_{n \to \infty} (1+\frac{x_n}{n})^n = 1$

Published on 02 Jan 2019 - 12:39

score 108 · Answer 12 · 2026-03-25 07:46:25

108

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Limlit of $\frac{x-x\ln(1+x)-\ln(1+x)}{x^3+x^2}$ at $0$ without l'Hôpital or Taylor series

Published on 25 Mar 2026 - 7:46

score 216 · Answer 13 · 2019-01-05 09:18:52

216

Views

Limit without L'Hospital rule

Published on 05 Jan 2019 - 9:18

score 42 · Answer 14 · 2019-01-08 07:52:58

42

Views

Let $f:\mathbb{Q}\to \mathbb{R}$, $f(p/q)=a^{p/q}$ such that $a>1$. Prove that $\lim_{x\to 0}f(x)=1$

Published on 08 Jan 2019 - 7:52

score 85 · Answer 15 · 2019-01-08 18:14:37

85

Views

How to evaluate $\lim_{x\to 0} \frac {(\sin(2x)-2\sin(x))^4}{(3+\cos(2x)-4\cos(x))^3}$?

Published on 08 Jan 2019 - 18:14

List Question

How do I solve $\lim \limits_{x \to \frac{π}{3}} \frac{2 \sin x - \sqrt{3}}{\cos \frac{3x}{2}}$

without L'Hospital's rule find the $\lim_{x\to 0+} (\csc x)^{\sin^2 x}$

Prove: $\lim\limits_{x\to\infty}\left(\sin^2\left(\frac{1}{x}\right)+\cos\frac1x\right)^{x^{2}}=\sqrt{e}$

Trouble with a sequence limit

How to calculate $ \lim_{x\to 0} (\frac{(5x + 1)^{20} - (20x + 1)^{5}}{\sqrt[5]{1 + 20x^{2}}-1}) $ without the rule of L'Hôpital?

Why L'Hospital Rule cannot apply in calculating $\lim_{x\rightarrow \infty}{(\cos {\frac{1}{x}} + \sin {\frac{1}{x^2}})^{\frac{1}{x^2}}}$

How to compute $\lim \limits_{x\to \infty} ((2x^3-2x^2+x)e^{1/x}-\sqrt{x^6+3})$ through Taylor series

How can I evaluate the left limit of this function?

Calculating $\lim\limits_{j \to \infty} \frac{j^{j/2}}{j!}$

How to find trigonometric limit $ \lim_{x\to π} \frac{\sin x}{x^2 - π^2} $

Show that if $\lim_{n \to \infty} x_n = 0$ if follows that $\lim_{n \to \infty} (1+\frac{x_n}{n})^n = 1$

Limlit of $\frac{x-x\ln(1+x)-\ln(1+x)}{x^3+x^2}$ at $0$ without l'Hôpital or Taylor series

Limit without L'Hospital rule

Let $f:\mathbb{Q}\to \mathbb{R}$, $f(p/q)=a^{p/q}$ such that $a>1$. Prove that $\lim_{x\to 0}f(x)=1$

How to evaluate $\lim_{x\to 0} \frac {(\sin(2x)-2\sin(x))^4}{(3+\cos(2x)-4\cos(x))^3}$?

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