Question

Can we work with $(\forall\epsilon>0)(\mu\in\mathbb R^+)"\mu\epsilon"$ in convergence definition and examples instead of $"\forall\epsilon>0"$?

score 77 · Answer 1 · 2017-03-29 19:55:19

77

Views

Can we work with $(\forall\epsilon>0)(\mu\in\mathbb R^+)"\mu\epsilon"$ in convergence definition and examples instead of $"\forall\epsilon>0"$?

Published on 29 Mar 2017 - 19:55

score 93 · Answer 2 · 2017-03-30 21:41:24

93

Views

Proof that $\varepsilon$-arguments are valid

Published on 30 Mar 2017 - 21:41

score 100 · Answer 3 · 2017-03-31 01:27:42

100

Views

How to Finish Epsilon-Delta Proof?

Published on 31 Mar 2017 - 1:27

score 157 · Answer 4 · 2017-04-01 12:33:09

157

Views

Limit question: $\lim_{x \rightarrow 2} \frac{x+1}{x+2} = \frac{3}{4}$

Published on 01 Apr 2017 - 12:33

score 334 · Answer 5 · 2017-04-02 22:11:38

334

Views

Prove that $\lim\limits_{x\rightarrow 4} \sqrt{2x+7} = \sqrt{15}$.

Published on 02 Apr 2017 - 22:11

score 499 · Answer 6 · 2017-04-02 22:37:35

499

Views

Precise proof of ratio test.

Published on 02 Apr 2017 - 22:37

score 2.9k · Answer 7 · 2026-03-29 16:33:05

2.9k

Views

squeeze theorem proof, using the same epsilon

Published on 29 Mar 2026 - 16:33

score 104 · Answer 8 · 2017-04-05 04:17:40

104

Views

Prove that the sequence in the metric space $(\Bbb N, d)$ with the property that as $j\rightarrow\infty$, $n_j\rightarrow\infty$ diverges?

Published on 05 Apr 2017 - 4:17

score 26 · Answer 9 · 2017-04-06 00:34:18

26

Views

"Strange" inequality derived from continuity

Published on 06 Apr 2017 - 0:34

score 356 · Answer 10 · 2017-04-08 21:22:12

356

Views

Showing that $\frac{1}{x^2}$ is continuous at a given point.

Published on 08 Apr 2017 - 21:22

score 85 · Answer 11 · 2023-01-31 09:56:34

85

Views

If $\lim_{n\to\infty} a_n=a$, then $\lim_{n\to\infty}\sum_{k=0}^n\frac{a_k}{n+1}=a$

Published on 31 Jan 2023 - 9:56

score 68 · Answer 12 · 2023-02-02 18:12:58

68

Views

Is contact of two continuous function also continuous to a parameter?

Published on 02 Feb 2023 - 18:12

score 86 · Answer 13 · 2023-02-05 14:31:06

86

Views

Determining delta graphically from limit definition

Published on 05 Feb 2023 - 14:31

score 68 · Answer 14 · 2023-02-06 06:50:33

68

Views

Check an $\epsilon-\delta$ proof of $\lim_{ (x,y) \to (3,1)} \frac{x}{y} = 3$

Published on 06 Feb 2023 - 6:50

score 55 · Answer 15 · 2023-02-13 19:44:29

55

Views

Prove $\lim_{(x,y)\to (0,0)}\frac{x^2 y^2}{x^2+y^2}=0$ with epsilon-delta

Published on 13 Feb 2023 - 19:44

List Question

Can we work with $(\forall\epsilon>0)(\mu\in\mathbb R^+)"\mu\epsilon"$ in convergence definition and examples instead of $"\forall\epsilon>0"$?

Proof that $\varepsilon$-arguments are valid

How to Finish Epsilon-Delta Proof?

Limit question: $\lim_{x \rightarrow 2} \frac{x+1}{x+2} = \frac{3}{4}$

Prove that $\lim\limits_{x\rightarrow 4} \sqrt{2x+7} = \sqrt{15}$.

Precise proof of ratio test.

squeeze theorem proof, using the same epsilon

Prove that the sequence in the metric space $(\Bbb N, d)$ with the property that as $j\rightarrow\infty$, $n_j\rightarrow\infty$ diverges?

"Strange" inequality derived from continuity

Showing that $\frac{1}{x^2}$ is continuous at a given point.

If $\lim_{n\to\infty} a_n=a$, then $\lim_{n\to\infty}\sum_{k=0}^n\frac{a_k}{n+1}=a$

Is contact of two continuous function also continuous to a parameter?

Determining delta graphically from limit definition

Check an $\epsilon-\delta$ proof of $\lim_{ (x,y) \to (3,1)} \frac{x}{y} = 3$

Prove $\lim_{(x,y)\to (0,0)}\frac{x^2 y^2}{x^2+y^2}=0$ with epsilon-delta

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