Question

Prove inverse of strictly monotone increasing function is continuous over the range of original function

score 3.7k · Answer 1 · 2026-03-25 19:04:13

3.7k

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Prove inverse of strictly monotone increasing function is continuous over the range of original function

Published on 25 Mar 2026 - 19:04

score 71 · Answer 2 · 2018-12-11 22:55:23

71

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I want to prove by $\epsilon - \delta$ definition this limit. Is it correct?

Published on 11 Dec 2018 - 22:55

score 2k · Answer 3 · 2018-12-11 23:07:08

2k

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Prove that the set of continuous real-valued functions on $[0,1]$ is a subspace of $\mathbb{R}^{[0,1]}$

Published on 11 Dec 2018 - 23:07

score 97 · Answer 4 · 2018-12-14 17:22:09

97

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Prove tht $f(x) = x^{2}$ is uniformly continuous on $\bigcup_{n = 1}^{\infty} [n, n + 1/n^{3}]$.

Published on 14 Dec 2018 - 17:22

score 82 · Answer 5 · 2018-12-15 11:50:46

82

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show that $\frac{\sqrt{2x}}{\sqrt{x+1}}$ is continuous at the point $x_0=1$

Published on 15 Dec 2018 - 11:50

score 276 · Answer 6 · 2018-12-16 19:23:08

276

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Explain why this definition of limit is incorrect

Published on 16 Dec 2018 - 19:23

score 174 · Answer 7 · 2018-12-16 20:03:03

174

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show that the function $f(x)= \frac{x^2+1}{x+1}$ is continuous at the point $x_0=1$

Published on 16 Dec 2018 - 20:03

score 151 · Answer 8 · 2018-12-19 04:26:35

151

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How to prove that $\lim_{x\rightarrow0}\frac{1}{2x+1}=1$ using $\delta-\epsilon$ definition?

Published on 19 Dec 2018 - 4:26

score 80 · Answer 9 · 2018-12-19 16:22:30

80

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$|f(a+h)-2f(a)+f(a-h')|<\varepsilon \Rightarrow f$ is continuous at a

Published on 19 Dec 2018 - 16:22

score 1k · Answer 10 · 2018-12-20 10:44:45

1k

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Show that if $\lim_{x\to c}(f(x))^2=0$ then $\lim_{x\to c}f(x)=0$

Published on 20 Dec 2018 - 10:44

score 70 · Answer 11 · 2018-12-21 15:43:46

70

Views

Can the archimedian postulate prove the limit of the series $1/n$ is $1$?

Published on 21 Dec 2018 - 15:43

score 48 · Answer 12 · 2018-12-25 19:12:10

48

Views

Difference between continuous over a set and continue in every point of that set

Published on 25 Dec 2018 - 19:12

score 1.1k · Answer 13 · 2018-12-26 11:57:46

1.1k

Views

$\frac{1}{x}$ not uniformly continuous

Published on 26 Dec 2018 - 11:57

score 74 · Answer 14 · 2018-12-28 15:42:16

74

Views

Is $F(x)=\frac{x}{x+1}$ for $x\in [0,1)$, $F(1)=\frac{1}{2}$ continuous?

Published on 28 Dec 2018 - 15:42

score 953 · Answer 15 · 2018-12-29 02:26:57

953

Views

Delta Epsilon Proof of $\lim_{x\to\infty}\frac{\ln{x}^2}{x}=0$

Published on 29 Dec 2018 - 2:26

List Question

Prove inverse of strictly monotone increasing function is continuous over the range of original function

I want to prove by $\epsilon - \delta$ definition this limit. Is it correct?

Prove that the set of continuous real-valued functions on $[0,1]$ is a subspace of $\mathbb{R}^{[0,1]}$

Prove tht $f(x) = x^{2}$ is uniformly continuous on $\bigcup_{n = 1}^{\infty} [n, n + 1/n^{3}]$.

show that $\frac{\sqrt{2x}}{\sqrt{x+1}}$ is continuous at the point $x_0=1$

Explain why this definition of limit is incorrect

show that the function $f(x)= \frac{x^2+1}{x+1}$ is continuous at the point $x_0=1$

How to prove that $\lim_{x\rightarrow0}\frac{1}{2x+1}=1$ using $\delta-\epsilon$ definition?

$|f(a+h)-2f(a)+f(a-h')|<\varepsilon \Rightarrow f$ is continuous at a

Show that if $\lim_{x\to c}(f(x))^2=0$ then $\lim_{x\to c}f(x)=0$

Can the archimedian postulate prove the limit of the series $1/n$ is $1$?

Difference between continuous over a set and continue in every point of that set

$\frac{1}{x}$ not uniformly continuous

Is $F(x)=\frac{x}{x+1}$ for $x\in [0,1)$, $F(1)=\frac{1}{2}$ continuous?

Delta Epsilon Proof of $\lim_{x\to\infty}\frac{\ln{x}^2}{x}=0$

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