Question

What is a rigorous way of deducing $ A \le B \le A$ from $ A-\varepsilon \le B \le A+\varepsilon$?

score 48 · Answer 1 · 2019-12-29 11:19:40

48

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What is a rigorous way of deducing $ A \le B \le A$ from $ A-\varepsilon \le B \le A+\varepsilon$?

Published on 29 Dec 2019 - 11:19

score 1.2k · Answer 2 · 2019-12-31 11:10:10

1.2k

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Proving $\lim_{x\to 0} f(x) = \lim_{x\to 0} f(x^3)$.

Published on 31 Dec 2019 - 11:10

score 128 · Answer 3 · 2020-01-04 16:04:50

128

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Disproving a limit of composite functions using Epsilon proof

Published on 04 Jan 2020 - 16:04

score 92 · Answer 4 · 2020-01-08 14:56:25

92

Views

Prove $f:D \to \mathbb{R}, x \to x+\frac{1}{x}$ is continuous on $D:= [2,13]$

Published on 08 Jan 2020 - 14:56

score 32 · Answer 5 · 2020-01-09 01:30:41

32

Views

$\delta > 0 $ so that $|f(x)-f(a)| < \epsilon$ follows for $f:D \to \mathbb{R}, x \to x+\frac{1}{x}$

Published on 09 Jan 2020 - 1:30

score 164 · Answer 6 · 2026-03-29 05:43:40

164

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Let $f(x)=x^{3} +5x +3$ Prove that $f(x)$ is uniformly continuous on any closed interval.

Published on 29 Mar 2026 - 5:43

score 355 · Answer 7 · 2020-01-09 13:59:53

355

Views

Spivak Calculus chapter 5(limits) problem 6 part (i)

Published on 09 Jan 2020 - 13:59

score 155 · Answer 8 · 2020-01-12 08:02:37

155

Views

Epsilon delta definition of limits with 2 variables and no E or D values

Published on 12 Jan 2020 - 8:02

score 53 · Answer 9 · 2020-01-12 20:36:39

53

Views

Prove limit by Cauchy definition $\lim_{x \to -4} \frac{x-10}{x+6} = -7$

Published on 12 Jan 2020 - 20:36

score 71 · Answer 10 · 2020-01-13 12:08:09

71

Views

Prove by epsilon delta definition $\lim_{x\to\infty} \sqrt x = \infty $

Published on 13 Jan 2020 - 12:08

score 80 · Answer 11 · 2026-03-26 11:04:13

80

Views

the validity of (ε, δ)-definition of limit

Published on 26 Mar 2026 - 11:04

score 94 · Answer 12 · 2020-01-22 07:22:17

94

Views

$\epsilon$-$\delta$ definition of the limit applied to nonlinear functions (teaching)

Published on 22 Jan 2020 - 7:22

score 1.8k · Answer 13 · 2020-01-27 18:11:12

1.8k

Views

Why must delta be defined in terms of epsilon only?

Published on 27 Jan 2020 - 18:11

score 313 · Answer 14 · 2020-01-27 22:21:14

313

Views

Having trouble with understanding proof of the sequential criterion for functional limits

Published on 27 Jan 2020 - 22:21

score 97 · Answer 15 · 2020-01-29 09:35:03

97

Views

Proving that $\lim_{x\rightarrow a} \sqrt[n]x = \sqrt[n]a$ using $\epsilon$ and $\delta$

Published on 29 Jan 2020 - 9:35

List Question

What is a rigorous way of deducing $ A \le B \le A$ from $ A-\varepsilon \le B \le A+\varepsilon$?

Proving $\lim_{x\to 0} f(x) = \lim_{x\to 0} f(x^3)$.

Disproving a limit of composite functions using Epsilon proof

Prove $f:D \to \mathbb{R}, x \to x+\frac{1}{x}$ is continuous on $D:= [2,13]$

$\delta > 0 $ so that $|f(x)-f(a)| < \epsilon$ follows for $f:D \to \mathbb{R}, x \to x+\frac{1}{x}$

Let $f(x)=x^{3} +5x +3$ Prove that $f(x)$ is uniformly continuous on any closed interval.

Spivak Calculus chapter 5(limits) problem 6 part (i)

Epsilon delta definition of limits with 2 variables and no E or D values

Prove limit by Cauchy definition $\lim_{x \to -4} \frac{x-10}{x+6} = -7$

Prove by epsilon delta definition $\lim_{x\to\infty} \sqrt x = \infty $

the validity of (ε, δ)-definition of limit

$\epsilon$-$\delta$ definition of the limit applied to nonlinear functions (teaching)

Why must delta be defined in terms of epsilon only?

Having trouble with understanding proof of the sequential criterion for functional limits

Proving that $\lim_{x\rightarrow a} \sqrt[n]x = \sqrt[n]a$ using $\epsilon$ and $\delta$

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