Question

Clarification on limit definition.

score 173 · Answer 1 · 2013-11-17 18:19:38

173

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Clarification on limit definition.

Published on 17 Nov 2013 - 18:19

score 2.2k · Answer 2 · 2013-11-22 04:18:33

2.2k

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Proving $\lim_{x\to 3} (x^2-5x+1)=-5$ by the $\epsilon -\delta$ definition of a limit.

Published on 22 Nov 2013 - 4:18

score 143 · Answer 3 · 2013-11-27 00:17:57

143

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Limit Proof Check: $\lim _{x \to a} x^4 = a^4$

Published on 27 Nov 2013 - 0:17

score 104 · Answer 4 · 2013-12-15 22:13:18

104

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Prove using the epsilon-delta definition that $ \lim\limits_{x\to 0}\ \frac{1+x}{2-x}=\frac12$

Published on 15 Dec 2013 - 22:13

score 2.4k · Answer 5 · 2013-12-21 00:19:30

2.4k

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Showing $f_n(x):=\frac{x}{1+n^2x^2}$ uniformly convergent in $\mathbb R$ using $\epsilon-n_0$

Published on 21 Dec 2013 - 0:19

score 111 · Answer 6 · 2014-02-13 15:17:04

111

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Limit of a function by definition $\lim\limits_{x\to0} \frac{x^2-1}{2x^2-x-1}=1$

Published on 13 Feb 2014 - 15:17

score 5.9k · Answer 7 · 2014-02-26 01:53:43

5.9k

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Prove that $\lim_{x\to a}f(x)=L$ implies $\lim_{x\to a}\sqrt{f(x)}=\sqrt L$

Published on 26 Feb 2014 - 1:53

score 10.2k · Answer 8 · 2014-03-01 17:08:54

10.2k

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$\epsilon$-$\delta$ proof of $\lim f(x)g(x) = \lim f(x)\lim g(x)$ for $x\to a$

Published on 01 Mar 2014 - 17:08

score 3.3k · Answer 9 · 2014-03-02 18:58:55

3.3k

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Another Epsilon-N Limit Proof Question

Published on 02 Mar 2014 - 18:58

score 84 · Answer 10 · 2026-04-04 01:24:18

84

Views

Prove that $(\Bbb R^n,\overline{d})$ is a complete metric space

Published on 04 Apr 2026 - 1:24

score 166 · Answer 11 · 2017-04-11 13:45:36

166

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Understanding a proof

Published on 11 Apr 2017 - 13:45

score 81 · Answer 12 · 2017-04-11 14:20:59

81

Views

verifing a limit with definition; finding delta when the interval is not circular ...

Published on 11 Apr 2017 - 14:20

score 477 · Answer 13 · 2017-04-11 19:43:33

477

Views

Compound Inequality to Absolute Value assumption in Epsilon-Delta problem

Published on 11 Apr 2017 - 19:43

score 654 · Answer 14 · 2017-04-11 23:16:15

654

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$\lim_{x \to 1} \frac{x^k - 1}{x - 1}$ using $\delta, \epsilon$

Published on 11 Apr 2017 - 23:16

score 74 · Answer 15 · 2017-04-14 13:46:34

74

Views

Why is this step necessary to prove $\lim_{x \to 2} x^2 = 4$?

Published on 14 Apr 2017 - 13:46

List Question

Clarification on limit definition.

Proving $\lim_{x\to 3} (x^2-5x+1)=-5$ by the $\epsilon -\delta$ definition of a limit.

Limit Proof Check: $\lim _{x \to a} x^4 = a^4$

Prove using the epsilon-delta definition that $ \lim\limits_{x\to 0}\ \frac{1+x}{2-x}=\frac12$

Showing $f_n(x):=\frac{x}{1+n^2x^2}$ uniformly convergent in $\mathbb R$ using $\epsilon-n_0$

Limit of a function by definition $\lim\limits_{x\to0} \frac{x^2-1}{2x^2-x-1}=1$

Prove that $\lim_{x\to a}f(x)=L$ implies $\lim_{x\to a}\sqrt{f(x)}=\sqrt L$

$\epsilon$-$\delta$ proof of $\lim f(x)g(x) = \lim f(x)\lim g(x)$ for $x\to a$

Another Epsilon-N Limit Proof Question

Prove that $(\Bbb R^n,\overline{d})$ is a complete metric space

Understanding a proof

verifing a limit with definition; finding delta when the interval is not circular ...

Compound Inequality to Absolute Value assumption in Epsilon-Delta problem

$\lim_{x \to 1} \frac{x^k - 1}{x - 1}$ using $\delta, \epsilon$

Why is this step necessary to prove $\lim_{x \to 2} x^2 = 4$?

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