Question

Proving a limit using the formal definition of a limit

score 110 · Answer 1 · 2017-11-18 20:19:11

110

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Proving a limit using the formal definition of a limit

Published on 18 Nov 2017 - 20:19

score 533 · Answer 2 · 2017-11-18 21:20:58

533

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Proving $ \lim\limits_{n\to\infty} \frac{8n^2-5}{4n^2+7} = 2$ using $\epsilon-\delta-$ definition.

Published on 18 Nov 2017 - 21:20

score 64 · Answer 3 · 2017-11-19 19:39:19

64

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$f:(-1,1)\rightarrow \mathbb{R}, \lim_{x\rightarrow 1} \frac{x+1}{x^2-1}$. Does $f$ have a limit at 1?

Published on 19 Nov 2017 - 19:39

score 511 · Answer 4 · 2017-11-20 20:48:47

511

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Delta Epsilon Continuity proof example

Published on 20 Nov 2017 - 20:48

score 5.8k · Answer 5 · 2017-11-22 06:07:14

5.8k

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Epsilon-delta derivative proof of $x^n$

Published on 22 Nov 2017 - 6:07

score 54 · Answer 6 · 2026-03-26 01:23:32

54

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For a given point $a=4$ and $\epsilon=0.01$ find a $\delta$ such that all x satisfying $0<|x-a|<\delta$ , the inequality

Published on 26 Mar 2026 - 1:23

score 530 · Answer 7 · 2017-11-25 18:53:58

530

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Showing proper divergence of the sequence $x_n=\frac{n}{\sqrt{n+1}}$ from definition

Published on 25 Nov 2017 - 18:53

score 285 · Answer 8 · 2017-11-27 22:15:58

285

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steps that show the epsilon and delta proof (multivariable)

Published on 27 Nov 2017 - 22:15

score 44 · Answer 9 · 2017-11-29 01:55:13

44

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Let $f: \Bbb{R} \to \Bbb{R}$ be defined as $f(x)=x^2 \; \forall x \in \Bbb{Q}$ and $f(x)=0 \; \forall x \in \Bbb{R} \setminus \Bbb{Q}$.

Published on 29 Nov 2017 - 1:55

score 116 · Answer 10 · 2026-04-03 17:12:17

116

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Show that $g(x)$ is not uniformly continuous on $(2,5)$

Published on 03 Apr 2026 - 17:12

score 756 · Answer 11 · 2026-03-30 03:55:38

756

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Proving that $a_n=\sqrt{n^2+n}-n$ converges, finding its limit and showing that its sequence ${(a_n)^{\infty}_{n=1}}$ is monotinic.

Published on 30 Mar 2026 - 3:55

score 150 · Answer 12 · 2026-04-03 17:12:18

150

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Give an example of a function which is continuous on $\mathbb{Q}\cap[2,4]$ but not uniformly continuous on the same set.

Published on 03 Apr 2026 - 17:12

score 104 · Answer 13 · 2026-04-03 17:06:07

104

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When is $\frac{f}{g}$ uniformly continuous?

Published on 03 Apr 2026 - 17:06

score 747 · Answer 14 · 2017-12-01 16:38:48

747

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Proving one sided limits

Published on 01 Dec 2017 - 16:38

score 2.3k · Answer 15 · 2026-04-03 17:12:19

2.3k

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Prove that sinx/x uniformly continuous at x [1; infinity) by using epsilon delta

Published on 03 Apr 2026 - 17:12

List Question

Proving a limit using the formal definition of a limit

Proving $ \lim\limits_{n\to\infty} \frac{8n^2-5}{4n^2+7} = 2$ using $\epsilon-\delta-$ definition.

$f:(-1,1)\rightarrow \mathbb{R}, \lim_{x\rightarrow 1} \frac{x+1}{x^2-1}$. Does $f$ have a limit at 1?

Delta Epsilon Continuity proof example

Epsilon-delta derivative proof of $x^n$

For a given point $a=4$ and $\epsilon=0.01$ find a $\delta$ such that all x satisfying $0<|x-a|<\delta$ , the inequality

Showing proper divergence of the sequence $x_n=\frac{n}{\sqrt{n+1}}$ from definition

steps that show the epsilon and delta proof (multivariable)

Let $f: \Bbb{R} \to \Bbb{R}$ be defined as $f(x)=x^2 \; \forall x \in \Bbb{Q}$ and $f(x)=0 \; \forall x \in \Bbb{R} \setminus \Bbb{Q}$.

Show that $g(x)$ is not uniformly continuous on $(2,5)$

Proving that $a_n=\sqrt{n^2+n}-n$ converges, finding its limit and showing that its sequence ${(a_n)^{\infty}_{n=1}}$ is monotinic.

Give an example of a function which is continuous on $\mathbb{Q}\cap[2,4]$ but not uniformly continuous on the same set.

When is $\frac{f}{g}$ uniformly continuous?

Proving one sided limits

Prove that sinx/x uniformly continuous at x [1; infinity) by using epsilon delta

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