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Help verifying $\lim \frac{2n^2}{n^3 +3} = 0$

score 1.8k · Answer 1 · 2018-07-12 21:20:43

1.8k

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Help verifying $\lim \frac{2n^2}{n^3 +3} = 0$

Published on 12 Jul 2018 - 21:20

score 135 · Answer 2 · 2018-07-14 05:10:13

135

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If $(x_n) \rightarrow 2$ then $(\frac{2x_n -1}{3}) \rightarrow 1$

Published on 14 Jul 2018 - 5:10

score 158 · Answer 3 · 2018-07-14 12:06:32

158

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Proving $f(x)=\sqrt{x}$ is uniformly continuous.

Published on 14 Jul 2018 - 12:06

score 361 · Answer 4 · 2018-07-15 02:44:55

361

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Proof of the Squeeze theorem for Sequences

Published on 15 Jul 2018 - 2:44

score 48 · Answer 5 · 2026-02-23 04:55:06

48

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How can I prove this sequence of functions pointwisely converges to zero using formal argument?

Published on 23 Feb 2026 - 4:55

score 151 · Answer 6 · 2018-07-17 21:04:07

151

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Proof that $\sum_{n = 0}^{\infty}\dfrac{1}{n(n+1)}$ converges to $1$

Published on 17 Jul 2018 - 21:04

score 5.3k · Answer 7 · 2018-07-18 01:12:46

5.3k

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Let $(x_n)$ and $(y_n)$ be given sequences and define $(z_n)$ to be the "shuffled" sequence...

Published on 18 Jul 2018 - 1:12

score 454 · Answer 8 · 2018-07-21 03:43:53

454

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Is it true that $\forall \epsilon>0, \exists \text{ infinitely many } n \in \mathbb{N}, s.t. |\sin(n) - 1| < \epsilon$?

Published on 21 Jul 2018 - 3:43

score 382 · Answer 9 · 2018-07-27 14:47:47

382

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Prove, using first principles, that $\lim\limits_{(x,y)\to(0,0)}{x.y^2=0}$

Published on 27 Jul 2018 - 14:47

score 4k · Answer 10 · 2018-07-27 23:01:39

4k

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Show that the $\lim \inf a_n = \lim \sup a_n$ if and only if $\lim a_n$ exists.

Published on 27 Jul 2018 - 23:01

score 34 · Answer 11 · 2018-07-30 22:41:19

34

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Reformulate continuity more rigorously

Published on 30 Jul 2018 - 22:41

score 71 · Answer 12 · 2018-07-31 04:24:02

71

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How to find $N(\varepsilon)$ such that $f(n)<\varepsilon$ $\forall n>N(\varepsilon)$

Published on 31 Jul 2018 - 4:24

score 69 · Answer 13 · 2018-08-02 07:22:43

69

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$(a_{(k_n)})_{n\in\mathbb N}$ converges to L?

Published on 02 Aug 2018 - 7:22

score 14.2k · Answer 14 · 2018-08-02 14:49:57

14.2k

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Show that 1/x is NOT uniformly continuous

Published on 02 Aug 2018 - 14:49

score 346 · Answer 15 · 2018-08-04 07:35:43

346

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Proving a Polynomial Limit where x → 0

Published on 04 Aug 2018 - 7:35

List Question

Help verifying $\lim \frac{2n^2}{n^3 +3} = 0$

If $(x_n) \rightarrow 2$ then $(\frac{2x_n -1}{3}) \rightarrow 1$

Proving $f(x)=\sqrt{x}$ is uniformly continuous.

Proof of the Squeeze theorem for Sequences

How can I prove this sequence of functions pointwisely converges to zero using formal argument?

Proof that $\sum_{n = 0}^{\infty}\dfrac{1}{n(n+1)}$ converges to $1$

Let $(x_n)$ and $(y_n)$ be given sequences and define $(z_n)$ to be the "shuffled" sequence...

Is it true that $\forall \epsilon>0, \exists \text{ infinitely many } n \in \mathbb{N}, s.t. |\sin(n) - 1| < \epsilon$?

Prove, using first principles, that $\lim\limits_{(x,y)\to(0,0)}{x.y^2=0}$

Show that the $\lim \inf a_n = \lim \sup a_n$ if and only if $\lim a_n$ exists.

Reformulate continuity more rigorously

How to find $N(\varepsilon)$ such that $f(n)<\varepsilon$ $\forall n>N(\varepsilon)$

$(a_{(k_n)})_{n\in\mathbb N}$ converges to L?

Show that 1/x is NOT uniformly continuous

Proving a Polynomial Limit where x → 0

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