List questions from epsilon-delta

Published on 26 Nov 2020 - 18:57

52

Views

$\lim _{x\rightarrow 0^{-}}e^\left(1/x\right)=0$ ($\delta-\varepsilon$ definition)

Published on 29 Nov 2020 - 17:07

142

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Prove $\lim_{x\to 0}$ of piecewise $f(x)=1$ if $x=1/n$ where $n\in \mathbb{Z}$ or $0$ otherwise on $[-1,1]$ doesn't exist.

Published on 26 Mar 2026 - 12:38

172

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Use of definition of limit to prove $\lim_{x→2} \dfrac{x}{x^2-2}=1$

Published on 01 Dec 2020 - 18:43

81

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Use of definition of limit to prove $\displaystyle\lim_{x→2} \sqrt[3]{x}= \sqrt[3]{2}$

Published on 02 Dec 2020 - 23:33

114

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Proving limit using definition

Published on 02 Apr 2026 - 2:47

85

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$[f(x)]^2$ being continuous should not imply that $f(x)$ is continuous

Published on 03 Dec 2020 - 18:37

603

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Proving a statement using the definition of a limit

Published on 05 Dec 2020 - 13:15

57

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Prove that $\lim_{x\to a} \sqrt{9-\sqrt{9-x^2}}=\sqrt{9-\sqrt{9-a^2}}$ using the epsilon-delta definition.

Published on 08 Dec 2020 - 5:40

460

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Show |x| is not differentiable at x=0 using delta epsilon

Published on 08 Dec 2020 - 9:01

361

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prove a statement with implies and limits using epsilon.

Published on 09 Dec 2020 - 18:28

124

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Proving limit of quadratic using formal definition without explicitly given f(x)

Published on 09 Dec 2020 - 19:09

44

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Proving that the exponential function is continious at $0$

Published on 11 Dec 2020 - 9:01

58

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multiplying a convergent sequence by a convergent series

Published on 28 Mar 2026 - 10:17

55

Views

How can I prove $\lim_{(x,y)\rightarrow(3,5)}\sqrt[3]{x+y}=2$ by definition?

Published on 12 Dec 2020 - 14:19

List Question

Prove that following limit exists

$\lim _{x\rightarrow 0^{-}}e^\left(1/x\right)=0$ ($\delta-\varepsilon$ definition)

Prove $\lim_{x\to 0}$ of piecewise $f(x)=1$ if $x=1/n$ where $n\in \mathbb{Z}$ or $0$ otherwise on $[-1,1]$ doesn't exist.

Use of definition of limit to prove $\lim_{x→2} \dfrac{x}{x^2-2}=1$

Use of definition of limit to prove $\displaystyle\lim_{x→2} \sqrt[3]{x}= \sqrt[3]{2}$

Proving limit using definition

$[f(x)]^2$ being continuous should not imply that $f(x)$ is continuous

Proving a statement using the definition of a limit

Prove that $\lim_{x\to a} \sqrt{9-\sqrt{9-x^2}}=\sqrt{9-\sqrt{9-a^2}}$ using the epsilon-delta definition.

Show |x| is not differentiable at x=0 using delta epsilon

prove a statement with implies and limits using epsilon.

Proving limit of quadratic using formal definition without explicitly given f(x)

Proving that the exponential function is continious at $0$

multiplying a convergent sequence by a convergent series

How can I prove $\lim_{(x,y)\rightarrow(3,5)}\sqrt[3]{x+y}=2$ by definition?

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