List questions from limits-without-lhopital

Published on 14 Apr 2026 - 0:00

126

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Mistake in this calculation of limits

Published on 11 Apr 2026 - 5:43

36

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For which $a\in\mathbb{R}, \lim \limits_{x \to a}$ of given function exist?

Published on 14 Apr 2026 - 16:21

160

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Limit of succession

Published on 14 Apr 2026 - 3:12

98

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Finding $\lim_{x\to 0^-} \frac{e^{1/x}}{x}$

Published on 14 Apr 2026 - 4:46

160

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Proving limit using $\epsilon$ and $\delta$

Published on 14 Apr 2026 - 11:08

138

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Limit of two-variable function: ${\lim_{(x,y) \to (0,0)} \frac{e^{x(y+1)} -x -1}{\|(x,y)\|}}$

Published on 14 Apr 2026 - 21:07

4.4k

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Proof that $\lim_{x\to \infty} (1+(x/n))^n = e^x$ Using Monotone Convergence Theorem

Published on 15 Apr 2026 - 7:39

446

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How to prove a sequence diverges? $a_n^\infty,$ defined by $a_{n+1}=-1-a_n^{2},\qquad a_1=1$

Published on 16 Apr 2026 - 20:20

251

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Value of a limit inside another limit

Published on 11 Apr 2026 - 7:57

130

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Taking the limit of n(e^1/n −1) as n approaches infinity then proving it by the squeeze theorem

Published on 10 May 2026 - 12:34

1k

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Limits indeterminate & undefined form

Published on 12 Apr 2026 - 3:36

388

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Evaluating $\lim_{x\rightarrow 0}\frac{\cos(ax) - \cos(bx)}{\sin^2(x)}$

Published on 17 Apr 2026 - 5:29

402

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Limit of $\lim_{x\to0} \left(\frac{1}{x}-\cot x\right) $ without L'Hopital's rule

Published on 16 Apr 2026 - 14:55

89

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Prove that $\lim_{n\rightarrow\infty}\frac{exp(r)}{r^n}=\infty$ from the definition

Published on 14 Apr 2026 - 18:13

List Question

I need to solve a limit without using l'Hopital rule

Mistake in this calculation of limits

For which $a\in\mathbb{R}, \lim \limits_{x \to a}$ of given function exist?

Limit of succession

Finding $\lim_{x\to 0^-} \frac{e^{1/x}}{x}$

Proving limit using $\epsilon$ and $\delta$

Limit of two-variable function: ${\lim_{(x,y) \to (0,0)} \frac{e^{x(y+1)} -x -1}{\|(x,y)\|}}$

Proof that $\lim_{x\to \infty} (1+(x/n))^n = e^x$ Using Monotone Convergence Theorem

How to prove a sequence diverges? $a_n^\infty,$ defined by $a_{n+1}=-1-a_n^{2},\qquad a_1=1$

Value of a limit inside another limit

Taking the limit of n(e^1/n −1) as n approaches infinity then proving it by the squeeze theorem

Limits indeterminate & undefined form

Evaluating $\lim_{x\rightarrow 0}\frac{\cos(ax) - \cos(bx)}{\sin^2(x)}$

Limit of $\lim_{x\to0} \left(\frac{1}{x}-\cot x\right) $ without L'Hopital's rule

Prove that $\lim_{n\rightarrow\infty}\frac{exp(r)}{r^n}=\infty$ from the definition

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