List questions from limits-without-lhopital

Published on 12 May 2021 - 12:08

69

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How to evaluate $\lim\limits_{x \to \infty}\dfrac{\ln{\left(1+e^x\right)}}{x}$ without using L'Hôpital's rule?

Published on 14 May 2021 - 10:26

129

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Solve $\lim_{N\to\infty} \frac{\sum_{n=0}^N \sin^4 (5n)}{N}$

Published on 16 May 2021 - 6:16

60

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Find the value of $\lim_{x\to 0} \frac {(1+3x+2x^2)^{1/x} - (1+3x-2x^2)^{1/x}}{x}$

Published on 16 May 2021 - 13:51

159

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$\lim_{x\to 0} \left(\int_0^1 3y+2(1-y)^xdy\right)^{1/x}$

Published on 19 May 2021 - 17:11

243

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$\lim_{n\to\infty}(\int_0^1 \frac{1}{1+x^n} dx)^n$

Published on 19 May 2021 - 18:53

83

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show limit by definition

Published on 25 May 2021 - 5:18

484

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L'Hospital's Rule for the indeterminate form $0^0$

Published on 27 Mar 2026 - 16:54

99

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How Should I correctly attempt $\lim\limits_{x\to2}\frac{|x^2-4|}{x-2}$

Published on 28 May 2021 - 7:09

36

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Limit of the given function

Published on 30 May 2021 - 2:07

116

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Evaluate trig limit without l'hopital's rule

Published on 31 May 2021 - 0:56

122

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Evaluating $\lim_{n\to\infty}\left(1 + \frac{\sin n}{5n + 1}\right)^{2n + 3}$ (a $1^\infty$ indeterminate form)

Published on 27 Mar 2026 - 18:26

68

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Limit without L'Hopital rule - help!

Published on 01 Jun 2021 - 0:29

67

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Where I am going wrong in the following evaluation of the following limit?

Published on 03 Jun 2021 - 16:21

379

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Finding the minimum value of $a+b$ if $\lim_{n\to\infty}\left(\frac{\left(1+\frac1n\right)^n}{\left(1-\frac1n\right)^n}-e^2\right)n^2=\frac{ae^2}{b}$

Published on 07 Jun 2021 - 12:02

List Question

Evaluate $\lim_{x\rightarrow -1^+}\frac{{e^{\frac{x}{x+1}}}}{x+1}$

How to evaluate $\lim\limits_{x \to \infty}\dfrac{\ln{\left(1+e^x\right)}}{x}$ without using L'Hôpital's rule?

Solve $\lim_{N\to\infty} \frac{\sum_{n=0}^N \sin^4 (5n)}{N}$

Find the value of $\lim_{x\to 0} \frac {(1+3x+2x^2)^{1/x} - (1+3x-2x^2)^{1/x}}{x}$

$\lim_{x\to 0} \left(\int_0^1 3y+2(1-y)^xdy\right)^{1/x}$

$\lim_{n\to\infty}(\int_0^1 \frac{1}{1+x^n} dx)^n$

show limit by definition

L'Hospital's Rule for the indeterminate form $0^0$

How Should I correctly attempt $\lim\limits_{x\to2}\frac{|x^2-4|}{x-2}$

Limit of the given function

Evaluate trig limit without l'hopital's rule

Evaluating $\lim_{n\to\infty}\left(1 + \frac{\sin n}{5n + 1}\right)^{2n + 3}$ (a $1^\infty$ indeterminate form)

Limit without L'Hopital rule - help!

Where I am going wrong in the following evaluation of the following limit?

Finding the minimum value of $a+b$ if $\lim_{n\to\infty}\left(\frac{\left(1+\frac1n\right)^n}{\left(1-\frac1n\right)^n}-e^2\right)n^2=\frac{ae^2}{b}$

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