Question

Prove $\{n^2\}_{n=1}^{\infty}$ is not convergent

score 1k · Answer 1 · 2015-03-31 12:08:58

1k

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Prove $\{n^2\}_{n=1}^{\infty}$ is not convergent

Published on 31 Mar 2015 - 12:08

score 507 · Answer 2 · 2015-03-31 22:00:28

507

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Manipulating inequalities in epsilon delta

Published on 31 Mar 2015 - 22:00

score 255 · Answer 3 · 2015-03-31 23:50:21

255

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Simple convergence proof

Published on 31 Mar 2015 - 23:50

score 82 · Answer 4 · 2015-04-02 11:27:57

82

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Proof that polynom $P:\mathbb{R}^n\to\mathbb{R}$ is continuous

Published on 02 Apr 2015 - 11:27

score 134 · Answer 5 · 2015-04-02 11:44:23

134

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T/F: $\forall \epsilon , \exists \delta \gt 0$ s.t. $\left| f(x)-f(a) \right| \lt \epsilon \implies \left| x-a \right| \lt \delta $

Published on 02 Apr 2015 - 11:44

score 16.8k · Answer 6 · 2015-04-06 13:29:04

16.8k

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Is this Epsilon-Delta approach to prove that $e^x$ is continuous correct?

Published on 06 Apr 2015 - 13:29

score 446 · Answer 7 · 2015-04-06 16:45:15

446

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Prove that $\lim_{x \rightarrow \infty} \frac{x^2+3}{4x^2-4x+8} = \frac{1}{4}$ using the $\epsilon$-$\delta $ definition of a limit.

Published on 06 Apr 2015 - 16:45

score 3.1k · Answer 8 · 2015-04-06 21:36:00

3.1k

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If $\lim_{n\to\infty}a_n=L$ and $f$ is continuous at $L$, then $\lim_{n\to\infty}f(a_n)=f(L)$. Is this true?

Published on 06 Apr 2015 - 21:36

score 49 · Answer 9 · 2015-04-07 14:00:22

49

Views

Epsilon and delta confusion

Published on 07 Apr 2015 - 14:00

score 519 · Answer 10 · 2015-04-08 16:00:53

519

Views

How to prove this limit using epsilon delta method?

Published on 08 Apr 2015 - 16:00

score 7k · Answer 11 · 2015-04-09 22:15:04

7k

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Proving $\lim_{x\to c}x^3=c^3$ for any $c\in\mathbb R$ using $\epsilon$-$\delta$ definition

Published on 09 Apr 2015 - 22:15

score 1k · Answer 12 · 2015-04-16 22:22:22

1k

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Prove $\lim\limits_{n \to \infty} \frac{2n^2+2}{3n^3+1}=0$ directly from the definition of limit.

Published on 16 Apr 2015 - 22:22

score 279 · Answer 13 · 2015-04-18 01:19:08

279

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Using exclusively the definition of limit proof that $\lim_{x \to 0} \frac{x^3-2x+x}{\sin(x)} = -1$

Published on 18 Apr 2015 - 1:19

score 105 · Answer 14 · 2015-04-18 20:15:57

105

Views

Real Analysis: Continuity

Published on 18 Apr 2015 - 20:15

score 70 · Answer 15 · 2026-04-01 00:23:57

70

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Prove this function is uniformly continuous by verifying the $\epsilon$-$\delta$ property?

Published on 01 Apr 2026 - 0:23

List Question

Prove $\{n^2\}_{n=1}^{\infty}$ is not convergent

Manipulating inequalities in epsilon delta

Simple convergence proof

Proof that polynom $P:\mathbb{R}^n\to\mathbb{R}$ is continuous

T/F: $\forall \epsilon , \exists \delta \gt 0$ s.t. $\left| f(x)-f(a) \right| \lt \epsilon \implies \left| x-a \right| \lt \delta $

Is this Epsilon-Delta approach to prove that $e^x$ is continuous correct?

Prove that $\lim_{x \rightarrow \infty} \frac{x^2+3}{4x^2-4x+8} = \frac{1}{4}$ using the $\epsilon$-$\delta $ definition of a limit.

If $\lim_{n\to\infty}a_n=L$ and $f$ is continuous at $L$, then $\lim_{n\to\infty}f(a_n)=f(L)$. Is this true?

Epsilon and delta confusion

How to prove this limit using epsilon delta method?

Proving $\lim_{x\to c}x^3=c^3$ for any $c\in\mathbb R$ using $\epsilon$-$\delta$ definition

Prove $\lim\limits_{n \to \infty} \frac{2n^2+2}{3n^3+1}=0$ directly from the definition of limit.

Using exclusively the definition of limit proof that $\lim_{x \to 0} \frac{x^3-2x+x}{\sin(x)} = -1$

Real Analysis: Continuity

Prove this function is uniformly continuous by verifying the $\epsilon$-$\delta$ property?

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