Question

Use $\varepsilon$-$\delta$ to prove $\lim_{x\to 1} \frac{1}{x^2} = 1$

score 70 · Answer 1 · 2026-04-02 06:19:28

70

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Use $\varepsilon$-$\delta$ to prove $\lim_{x\to 1} \frac{1}{x^2} = 1$

Published on 02 Apr 2026 - 6:19

score 56 · Answer 2 · 2021-03-10 19:04:58

56

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Limits of $f: E \to \mathbb R$

Published on 10 Mar 2021 - 19:04

score 172 · Answer 3 · 2021-03-10 21:30:56

172

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$f (x) = 1$ if the digit $9$ appears in the decimal representation of $x$ and $f (x) = 0$ otherwise — show that $f$ is continuous

Published on 10 Mar 2021 - 21:30

score 1k · Answer 4 · 2021-03-11 19:55:41

1k

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Epsilon-delta proofs

Published on 11 Mar 2021 - 19:55

score 104 · Answer 5 · 2026-04-01 14:32:57

104

Views

Limit of sequences of $C^{\infty}$ function

Published on 01 Apr 2026 - 14:32

score 599 · Answer 6 · 2026-02-25 20:17:23

599

Views

What does point-wise convergence in the sup norm mean?

Published on 25 Feb 2026 - 20:17

score 114 · Answer 7 · 2021-03-13 15:17:43

114

Views

Prove the $\lim_{x \to -1} x^2 + 4x + 2 = 0$ is wrong by negating the $\epsilon-\delta$ definition of limit

Published on 13 Mar 2021 - 15:17

score 650 · Answer 8 · 2021-03-13 19:50:39

650

Views

$\delta$-response for challenging the $\lim_{x \to 10} \frac{1}{[[x]]} = \frac{1}{10}$ with $\epsilon=\frac{1}{2}$

Published on 13 Mar 2021 - 19:50

score 397 · Answer 9 · 2021-03-14 01:56:54

397

Views

If $\lim_{n \to \infty} |a_n| = |L|$ then $\lim_{n \to \infty} a_n = L$

Published on 14 Mar 2021 - 1:56

score 251 · Answer 10 · 2021-03-14 18:49:26

251

Views

Using the Epsilon-N Definition of limits of sequences

Published on 14 Mar 2021 - 18:49

score 186 · Answer 11 · 2021-03-14 19:15:44

186

Views

If $\lim_{x \to x_0} f(x) = f(x_0)$, as $x \to x_0$, can we always say $f(x) \to f(x_0)$

Published on 14 Mar 2021 - 19:15

score 41 · Answer 12 · 2026-02-23 20:43:28

41

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How to show $\lim _{n \rightarrow \infty} \int_{1-\frac{1}{n}}^{1}f(x) d x=0$

Published on 23 Feb 2026 - 20:43

score 88 · Answer 13 · 2021-03-15 20:13:54

Show directly from the $\epsilon$-$\delta$ definition that $\lim_{x\to0}\frac{\sin(3x)}{3x} = 1$ given $\lim_{x\to0}\frac{\sin(x)}{x} = 1$

score 105 · Answer 14 · 2021-03-16 00:36:39

105

Views

Prove $\displaystyle \dfrac{n}{n + 1} > M$ whenever $n > N$ for some integer $N$

Published on 16 Mar 2021 - 0:36

score 259 · Answer 15 · 2021-03-17 11:11:43

259

Views

Limit exists with definition but not with polar coordinates

Published on 17 Mar 2021 - 11:11

List Question

Use $\varepsilon$-$\delta$ to prove $\lim_{x\to 1} \frac{1}{x^2} = 1$

Limits of $f: E \to \mathbb R$

$f (x) = 1$ if the digit $9$ appears in the decimal representation of $x$ and $f (x) = 0$ otherwise — show that $f$ is continuous

Epsilon-delta proofs

Limit of sequences of $C^{\infty}$ function

What does point-wise convergence in the sup norm mean?

Prove the $\lim_{x \to -1} x^2 + 4x + 2 = 0$ is wrong by negating the $\epsilon-\delta$ definition of limit

$\delta$-response for challenging the $\lim_{x \to 10} \frac{1}{[[x]]} = \frac{1}{10}$ with $\epsilon=\frac{1}{2}$

If $\lim_{n \to \infty} |a_n| = |L|$ then $\lim_{n \to \infty} a_n = L$

Using the Epsilon-N Definition of limits of sequences

If $\lim_{x \to x_0} f(x) = f(x_0)$, as $x \to x_0$, can we always say $f(x) \to f(x_0)$

How to show $\lim _{n \rightarrow \infty} \int_{1-\frac{1}{n}}^{1}f(x) d x=0$

Show directly from the $\epsilon$-$\delta$ definition that $\lim_{x\to0}\frac{\sin(3x)}{3x} = 1$ given $\lim_{x\to0}\frac{\sin(x)}{x} = 1$

Prove $\displaystyle \dfrac{n}{n + 1} > M$ whenever $n > N$ for some integer $N$

Limit exists with definition but not with polar coordinates

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