Question

Limit of $x^2\sin\left(\ln\sqrt{\cos\frac{\pi}{x}}\right)$

score 1.9k · Answer 1 · 2015-02-27 08:12:16

1.9k

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Limit of $x^2\sin\left(\ln\sqrt{\cos\frac{\pi}{x}}\right)$

Published on 27 Feb 2015 - 8:12

score 64 · Answer 2 · 2015-02-28 17:12:40

64

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I need to show the following two limits

Published on 28 Feb 2015 - 17:12

score 202 · Answer 3 · 2015-03-02 09:15:04

202

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Find the limiting value of this sequence

Published on 02 Mar 2015 - 9:15

score 140 · Answer 4 · 2015-03-02 12:12:54

140

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How to calculate $\lim \limits_{x \to 0^{+}} (\sin x)^{e^{x}-1} $ with Taylor series?

Published on 02 Mar 2015 - 12:12

score 48 · Answer 5 · 2026-03-30 16:01:48

48

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Simplify the function of x

Published on 30 Mar 2026 - 16:01

score 259 · Answer 6 · 2015-03-05 12:15:21

259

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Show that if $x_n\rightarrow\ x_0^{-}$ and $y_n\rightarrow\ x_0^{+}$ then $ \lim \limits_{n \to \infty} \frac{f(y_n)-f(x_n)}{y_n-x_n} = f^\prime(x_0)$

Published on 05 Mar 2015 - 12:15

score 1.8k · Answer 7 · 2015-03-06 16:13:43

1.8k

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Limit of a sequence. Let $ { \{a_n \}} $ be a sequence of real numbers. Then $ \lim_{n \to \infty} a_n $ exists if and only if

Published on 06 Mar 2015 - 16:13

score 822 · Answer 8 · 2015-03-07 11:46:44

822

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$\lim_{x\to0}\frac{e^x-1-x}{x^2}$ using only rules of algebra of limits.

Published on 07 Mar 2015 - 11:46

score 287 · Answer 9 · 2015-03-07 17:58:24

287

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The limit $\lim_{x\to 0}\frac{e^{x\ln(x)}-1}{x}$

Published on 07 Mar 2015 - 17:58

score 414 · Answer 10 · 2015-03-10 20:36:34

414

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Tricky Limit Problem involving e

Published on 10 Mar 2015 - 20:36

score 71 · Answer 11 · 2015-03-11 15:24:12

71

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Finding $ \lim_{x\to -2}~~ \sin(\frac{\pi x}{2})\frac{x^2+1}{x+2}$.

Published on 11 Mar 2015 - 15:24

score 1.6k · Answer 12 · 2015-03-16 01:39:14

1.6k

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How can I find $\lim_{x \to 0}\left(\frac{e^{2\sin x}-1}{x}\right)$ without l'Hopital's Rule?

Published on 16 Mar 2015 - 1:39

score 539 · Answer 13 · 2015-03-17 14:40:22

539

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The limit : $ \lim _{x \to \infty } \sqrt{x^2 +x} - \sqrt{x^2 +1} $

Published on 17 Mar 2015 - 14:40

score 82 · Answer 14 · 2015-03-18 12:12:57

82

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Better way to do $\lim_{n\to\infty}\frac{(3n-1)^{1/n}}{{\sqrt{2}}^{1/n}}$

Published on 18 Mar 2015 - 12:12

score 264 · Answer 15 · 2015-03-18 14:52:10

264

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Calculate the limit $\lim_{x\to 1}\frac{\sqrt[359]{x} - 1}{\sqrt[5]{x} - 1}$

Published on 18 Mar 2015 - 14:52

List Question

Limit of $x^2\sin\left(\ln\sqrt{\cos\frac{\pi}{x}}\right)$

I need to show the following two limits

Find the limiting value of this sequence

How to calculate $\lim \limits_{x \to 0^{+}} (\sin x)^{e^{x}-1} $ with Taylor series?

Simplify the function of x

Show that if $x_n\rightarrow\ x_0^{-}$ and $y_n\rightarrow\ x_0^{+}$ then $ \lim \limits_{n \to \infty} \frac{f(y_n)-f(x_n)}{y_n-x_n} = f^\prime(x_0)$

Limit of a sequence. Let $ { \{a_n \}} $ be a sequence of real numbers. Then $ \lim_{n \to \infty} a_n $ exists if and only if

$\lim_{x\to0}\frac{e^x-1-x}{x^2}$ using only rules of algebra of limits.

The limit $\lim_{x\to 0}\frac{e^{x\ln(x)}-1}{x}$

Tricky Limit Problem involving e

Finding $ \lim_{x\to -2}~~ \sin(\frac{\pi x}{2})\frac{x^2+1}{x+2}$.

How can I find $\lim_{x \to 0}\left(\frac{e^{2\sin x}-1}{x}\right)$ without l'Hopital's Rule?

The limit : $ \lim _{x \to \infty } \sqrt{x^2 +x} - \sqrt{x^2 +1} $

Better way to do $\lim_{n\to\infty}\frac{(3n-1)^{1/n}}{{\sqrt{2}}^{1/n}}$

Calculate the limit $\lim_{x\to 1}\frac{\sqrt[359]{x} - 1}{\sqrt[5]{x} - 1}$

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