Question

Prove that $\lim_{(x,y)\rightarrow (1,1)}x^2+y^2$ is not $3$

score 70 · Answer 1 · 2021-08-29 11:19:16

70

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Prove that $\lim_{(x,y)\rightarrow (1,1)}x^2+y^2$ is not $3$

Published on 29 Aug 2021 - 11:19

score 186 · Answer 2 · 2021-08-31 00:14:23

186

Views

Use Epsilon Definition of Limit to Prove Limit Exists

Published on 31 Aug 2021 - 0:14

score 262 · Answer 3 · 2021-09-01 07:21:07

262

Views

Prove that $ \lim_{x\to 0}x^x=1$.

Published on 01 Sep 2021 - 7:21

score 66 · Answer 4 · 2021-09-02 22:00:47

66

Views

Finding a $\delta$ corresponding to $\epsilon = 0.01$ for $f(x) = \sqrt{x}$

Published on 02 Sep 2021 - 22:00

score 291 · Answer 5 · 2026-03-30 05:13:15

291

Views

Completeness for a given metric on the sequences of $0s$ and $1s$

Published on 30 Mar 2026 - 5:13

score 79 · Answer 6 · 2026-04-05 18:39:49

79

Views

Prove (only with definition) that $f(x)=\frac{x^3+1}{x^2}, x>0$ is not uniformly continuous

Published on 05 Apr 2026 - 18:39

score 252 · Answer 7 · 2021-09-09 05:40:43

252

Views

As the limit of $n$ goes to infinity, prove that $x^n=0$ if $|x|<1$ using delta-epsilon definition

Published on 09 Sep 2021 - 5:40

score 139 · Answer 8 · 2021-09-10 09:46:52

139

Views

If $\lim_{x\to a}f(x)=L$, is the set $\{\delta\in\mathbb{R}:0<|x-a|<\delta\implies |f(x)-L|<\varepsilon\}$ always an interval?

Published on 10 Sep 2021 - 9:46

score 120 · Answer 9 · 2021-09-10 18:39:00

120

Views

Q: Epsilon-delta proof for $\lim_{x\to1} \frac{x}{x^2+1}=\frac{1}{2}$

Published on 10 Sep 2021 - 18:39

score 165 · Answer 10 · 2021-09-11 18:14:12

165

Views

My proof on sum of two sequences is real number?

Published on 11 Sep 2021 - 18:14

score 216 · Answer 11 · 2021-09-13 22:38:31

216

Views

Real Analysis Question: How to use epsilon-N definition to prove the limit exists.

Published on 13 Sep 2021 - 22:38

score 445 · Answer 12 · 2026-03-29 20:49:13

445

Views

Using $\delta$-$\varepsilon$ definition to prove stability for autonomous system

Published on 29 Mar 2026 - 20:49

score 88 · Answer 13 · 2021-09-16 09:03:06

88

Views

Proofs wether a limit exists or not.

Published on 16 Sep 2021 - 9:03

score 94 · Answer 14 · 2021-09-16 13:41:09

94

Views

if $\lim_{x \to \infty} f(x)=L$ and $\lim_{x \to \infty}g(x)=M$ then $\lim_{x\to \infty}f(x)/g(x)=L/M$

Published on 16 Sep 2021 - 13:41

score 109 · Answer 15 · 2021-09-18 20:55:52

109

Views

How can I show that $\lim_{x \to 0}\frac{e^{-\frac{1}{x^2}}}{x}=0$ by $\varepsilon, \delta$

Published on 18 Sep 2021 - 20:55

List Question

Prove that $\lim_{(x,y)\rightarrow (1,1)}x^2+y^2$ is not $3$

Use Epsilon Definition of Limit to Prove Limit Exists

Prove that $ \lim_{x\to 0}x^x=1$.

Finding a $\delta$ corresponding to $\epsilon = 0.01$ for $f(x) = \sqrt{x}$

Completeness for a given metric on the sequences of $0s$ and $1s$

Prove (only with definition) that $f(x)=\frac{x^3+1}{x^2}, x>0$ is not uniformly continuous

As the limit of $n$ goes to infinity, prove that $x^n=0$ if $|x|<1$ using delta-epsilon definition

If $\lim_{x\to a}f(x)=L$, is the set $\{\delta\in\mathbb{R}:0<|x-a|<\delta\implies |f(x)-L|<\varepsilon\}$ always an interval?

Q: Epsilon-delta proof for $\lim_{x\to1} \frac{x}{x^2+1}=\frac{1}{2}$

My proof on sum of two sequences is real number?

Real Analysis Question: How to use epsilon-N definition to prove the limit exists.

Using $\delta$-$\varepsilon$ definition to prove stability for autonomous system

Proofs wether a limit exists or not.

if $\lim_{x \to \infty} f(x)=L$ and $\lim_{x \to \infty}g(x)=M$ then $\lim_{x\to \infty}f(x)/g(x)=L/M$

How can I show that $\lim_{x \to 0}\frac{e^{-\frac{1}{x^2}}}{x}=0$ by $\varepsilon, \delta$

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