Question

Determine $\lim\limits_{x\to 0, x\neq 0}\frac{e^{\sin(x)}-1}{\sin(2x)}=\frac{1}{2}$ without using L'Hospital

score 727 · Answer 1 · 2017-12-25 21:40:58

727

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Determine $\lim\limits_{x\to 0, x\neq 0}\frac{e^{\sin(x)}-1}{\sin(2x)}=\frac{1}{2}$ without using L'Hospital

Published on 25 Dec 2017 - 21:40

score 229 · Answer 2 · 2017-12-25 21:51:02

229

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Calculate the limit: $\lim_{x\to \infty} (1-\frac{2x+1}{2x-1})^x$

Published on 25 Dec 2017 - 21:51

score 109 · Answer 3 · 2017-12-26 14:19:11

109

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Compute $\lim_{u\to 0}\frac{(u+1)^\tau-1}{u}$ without l'Hopital ($\tau>0$).

Published on 26 Dec 2017 - 14:19

score 133 · Answer 4 · 2017-12-26 18:02:46

133

Views

For $\alpha>1$ find $\lim_{n\to\infty} \sqrt[n]{\sqrt[2^n]{\alpha}-1}$

Published on 26 Dec 2017 - 18:02

score 977 · Answer 5 · 2017-12-28 15:41:30

977

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Find: $\lim_{x\to -\infty} \frac{\ln (1+e^x)}{x}$ (no L'Hospital)

Published on 28 Dec 2017 - 15:41

score 2.5k · Answer 6 · 2026-03-30 04:56:35

2.5k

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Why can we replace an infinitesimal in a limit with an equivalent infinitesimal?

Published on 30 Mar 2026 - 4:56

score 351 · Answer 7 · 2017-12-29 15:32:08

351

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Limit $\lim_{x\to \frac{\pi}{3}} \frac{\sin(x-\frac{\pi}{3})}{1-2 \cos{x}}$

Published on 29 Dec 2017 - 15:32

score 342 · Answer 8 · 2017-12-29 15:47:14

342

Views

Prove $\lim_{x \to \infty} (1+1/x)^x = e$ using sequences

Published on 29 Dec 2017 - 15:47

score 163 · Answer 9 · 2017-12-30 11:15:05

163

Views

Oblique asymptote of $f(x) = \frac{x\sqrt{x}}{\sqrt{x+2}}$

Published on 30 Dec 2017 - 11:15

score 3.7k · Answer 10 · 2017-12-30 16:29:53

3.7k

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Solve $ \lim _{x\to 0}\left(\frac{\sin x}{\sqrt{1-\cos x}}\right) $

Published on 30 Dec 2017 - 16:29

score 151 · Answer 11 · 2017-12-30 22:25:22

151

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Find: $ \lim_{x\to \infty}\frac{x-1}{\sqrt{x}}-\frac{x-1}{\sqrt{x+1}}$

Published on 30 Dec 2017 - 22:25

score 120 · Answer 12 · 2017-12-31 11:59:58

120

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Find: $\lim_{x\to -\infty} f(x)= \frac{x^2-\sqrt{x^4+1}}{x^3-\sqrt{x^6+1}}$ (no L'Hopital)

Published on 31 Dec 2017 - 11:59

score 154 · Answer 13 · 2017-12-31 15:27:31

154

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Find: $ \lim_{x\to \frac{\pi}{4}} \frac{\sin 4x}{1-\sqrt{2} \cos x}$ (no L'Hopital)

Published on 31 Dec 2017 - 15:27

score 4.4k · Answer 14 · 2018-01-01 13:30:02

4.4k

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Evaluate the limit $\lim_{x\to0}\left(\frac{\tan (x)+4\tan(2x)-3\tan(3x)}{x^2\tan(x)}\right)$ without using L'Hôpital's rule.

Published on 01 Jan 2018 - 13:30

score 146 · Answer 15 · 2018-01-01 17:49:47

146

Views

Find $\lim\limits_{n \rightarrow \infty}n\bigg(\cos \bigg(\frac {1}{\sqrt n} \bigg) - 1\bigg)$

Published on 01 Jan 2018 - 17:49

List Question

Determine $\lim\limits_{x\to 0, x\neq 0}\frac{e^{\sin(x)}-1}{\sin(2x)}=\frac{1}{2}$ without using L'Hospital

Calculate the limit: $\lim_{x\to \infty} (1-\frac{2x+1}{2x-1})^x$

Compute $\lim_{u\to 0}\frac{(u+1)^\tau-1}{u}$ without l'Hopital ($\tau>0$).

For $\alpha>1$ find $\lim_{n\to\infty} \sqrt[n]{\sqrt[2^n]{\alpha}-1}$

Find: $\lim_{x\to -\infty} \frac{\ln (1+e^x)}{x}$ (no L'Hospital)

Why can we replace an infinitesimal in a limit with an equivalent infinitesimal?

Limit $\lim_{x\to \frac{\pi}{3}} \frac{\sin(x-\frac{\pi}{3})}{1-2 \cos{x}}$

Prove $\lim_{x \to \infty} (1+1/x)^x = e$ using sequences

Oblique asymptote of $f(x) = \frac{x\sqrt{x}}{\sqrt{x+2}}$

Solve $ \lim _{x\to 0}\left(\frac{\sin x}{\sqrt{1-\cos x}}\right) $

Find: $ \lim_{x\to \infty}\frac{x-1}{\sqrt{x}}-\frac{x-1}{\sqrt{x+1}}$

Find: $\lim_{x\to -\infty} f(x)= \frac{x^2-\sqrt{x^4+1}}{x^3-\sqrt{x^6+1}}$ (no L'Hopital)

Find: $ \lim_{x\to \frac{\pi}{4}} \frac{\sin 4x}{1-\sqrt{2} \cos x}$ (no L'Hopital)

Evaluate the limit $\lim_{x\to0}\left(\frac{\tan (x)+4\tan(2x)-3\tan(3x)}{x^2\tan(x)}\right)$ without using L'Hôpital's rule.

Find $\lim\limits_{n \rightarrow \infty}n\bigg(\cos \bigg(\frac {1}{\sqrt n} \bigg) - 1\bigg)$

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