Question

Limits involving exponents

score 45 · Answer 1 · 2022-05-14 04:04:18

45

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Limits involving exponents

Published on 14 May 2022 - 4:04

score 55 · Answer 2 · 2022-05-15 15:09:27

55

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Other approaches to evaluate $\lim_{h\to 0} \frac{4^{x+h}+4^{x-h}-4^{x+\frac12}}{h^2}$

Published on 15 May 2022 - 15:09

score 92 · Answer 3 · 2022-05-16 06:15:47

92

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How to find $\lim_{x\to-\infty} \frac{\sqrt{x^2+2x}}{-x}$?

Published on 16 May 2022 - 6:15

score 70 · Answer 4 · 2022-05-17 16:46:26

70

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Solving $\lim_{t \to \infty} t\log(\frac{\frac{\log(\alpha + 1)}{t} - \frac{\log(t + \alpha)}{t}}{ 1 - \frac{1}{t(t + \alpha)}} + 1)$

Published on 17 May 2022 - 16:46

score 119 · Answer 5 · 2022-05-18 04:56:06

119

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Evaluate the common limit

Published on 18 May 2022 - 4:56

score 761 · Answer 6 · 2022-05-18 05:50:31

761

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Limit of sin(sin(sin(x)))

Published on 18 May 2022 - 5:50

score 76 · Answer 7 · 2022-05-19 17:33:06

76

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How do you find this limit with a relationship to $e$ using Taylor series?

Published on 19 May 2022 - 17:33

score 106 · Answer 8 · 2022-05-28 05:22:46

106

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Evaluating $\lim_{x \rightarrow 0} \frac{\sin(\pi x)(1-\cos(\pi x)}{x^2\sin(x)}$ without L'hôpital's rule

Published on 28 May 2022 - 5:22

score 625 · Answer 9 · 2022-05-30 16:35:13

625

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Elementary proof of $\lim_{n\to\infty}n(\sqrt[n]{n}-1)=\infty$

Published on 30 May 2022 - 16:35

score 81 · Answer 10 · 2022-06-02 00:10:28

81

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Evaluating $\lim_{x\to2}\frac{\sqrt[3]{x^2-x-1}-\sqrt{x^2-3x+3}}{x^3-8}$ without Hopital rule

Published on 02 Jun 2022 - 0:10

score 48 · Answer 11 · 2022-06-04 16:46:48

48

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Hint for proving that $\lim_{x \to 0} \log_{10}{|x|}$ does not exist

Published on 04 Jun 2022 - 16:46

score 144 · Answer 12 · 2022-06-08 05:24:05

144

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$L_1=\lim_{x\to 0}\dfrac{1-\cos x\cos 2x \cos 3x}{x^2}\;$ and $L_2=\lim_{x\to 0} \dfrac{1-(\cos x)^{{(\cos 2x)}^{(\cos 3x)}}}{x^2}\;$

Published on 08 Jun 2022 - 5:24

score 98 · Answer 13 · 2026-04-07 19:34:57

98

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Can we use $(1+x)^n = 1+nx$ where $x\to0$ and $n$ is $1/0$?

Published on 07 Apr 2026 - 19:34

score 73 · Answer 14 · 2026-04-09 06:28:31

73

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Is there a limit which is hard to compute without L'Hôpital's rule?

Published on 09 Apr 2026 - 6:28

score 68 · Answer 15 · 2022-06-16 15:50:09

68

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Evaluating $\lim_{x\to {0}}\frac{1}{x\arcsin x} - \frac{1}{x^2}$ without L'Hôpital's rule

Published on 16 Jun 2022 - 15:50

List Question

Limits involving exponents

Other approaches to evaluate $\lim_{h\to 0} \frac{4^{x+h}+4^{x-h}-4^{x+\frac12}}{h^2}$

How to find $\lim_{x\to-\infty} \frac{\sqrt{x^2+2x}}{-x}$?

Solving $\lim_{t \to \infty} t\log(\frac{\frac{\log(\alpha + 1)}{t} - \frac{\log(t + \alpha)}{t}}{ 1 - \frac{1}{t(t + \alpha)}} + 1)$

Evaluate the common limit

Limit of sin(sin(sin(x)))

How do you find this limit with a relationship to $e$ using Taylor series?

Evaluating $\lim_{x \rightarrow 0} \frac{\sin(\pi x)(1-\cos(\pi x)}{x^2\sin(x)}$ without L'hôpital's rule

Elementary proof of $\lim_{n\to\infty}n(\sqrt[n]{n}-1)=\infty$

Evaluating $\lim_{x\to2}\frac{\sqrt[3]{x^2-x-1}-\sqrt{x^2-3x+3}}{x^3-8}$ without Hopital rule

Hint for proving that $\lim_{x \to 0} \log_{10}{|x|}$ does not exist

$L_1=\lim_{x\to 0}\dfrac{1-\cos x\cos 2x \cos 3x}{x^2}\;$ and $L_2=\lim_{x\to 0} \dfrac{1-(\cos x)^{{(\cos 2x)}^{(\cos 3x)}}}{x^2}\;$

Can we use $(1+x)^n = 1+nx$ where $x\to0$ and $n$ is $1/0$?

Is there a limit which is hard to compute without L'Hôpital's rule?

Evaluating $\lim_{x\to {0}}\frac{1}{x\arcsin x} - \frac{1}{x^2}$ without L'Hôpital's rule

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