Question

$f'(x)\neq0 \Rightarrow$ f is monotonic

score 80 · Answer 1 · 2017-05-12 19:34:44

80

Views

$f'(x)\neq0 \Rightarrow$ f is monotonic

Published on 12 May 2017 - 19:34

score 50 · Answer 2 · 2017-05-13 03:47:37

50

Views

What is the exact limit of the following monotone sequence?

Published on 13 May 2017 - 3:47

score 105 · Answer 3 · 2017-05-16 15:31:39

105

Views

Increasing sequence of functions with subsequence that converges in $H^1$ and $L^2$; does the full sequence converge?

Published on 16 May 2017 - 15:31

score 80 · Answer 4 · 2017-05-17 06:21:06

80

Views

If $a<b$, the $\lim_{x\to a^+}f(x) \le \lim_{x\to b^-}f(x) $?

Published on 17 May 2017 - 6:21

score 666 · Answer 5 · 2017-05-19 08:47:28

666

Views

Prove that $(1+\frac{\log(x)}{x})^x$ is monotonically increasing function for $x \geq 1$

Published on 19 May 2017 - 8:47

score 164 · Answer 6 · 2017-05-29 13:44:07

164

Views

Is a quasiconvex function always the monotone image of a convex function?

Published on 29 May 2017 - 13:44

score 274 · Answer 7 · 2026-03-25 09:22:28

274

Views

Is every monotonic simple function a step function?

Published on 25 Mar 2026 - 9:22

score 90 · Answer 8 · 2017-06-07 06:20:22

90

Views

Doubt in discontinuities of a monotonic function.

Published on 07 Jun 2017 - 6:20

score 551 · Answer 9 · 2017-06-08 04:59:30

551

Views

Proof verification : $\lim_{x \to c^+}f(x)=\inf\{f(x): x>c\}$ for increasing $f$

Published on 08 Jun 2017 - 4:59

score 522 · Answer 10 · 2026-03-29 14:07:05

522

Views

Is the power of a positive strictly monotonic function convex/concave?

Published on 29 Mar 2026 - 14:07

score 90 · Answer 11 · 2017-06-09 06:57:14

90

Views

Proof verification : $f$ is continuous at $c$ $\Leftrightarrow$ $f$ has zero-jump at $c$ for increasing $f$

Published on 09 Jun 2017 - 6:57

score 59 · Answer 12 · 2017-06-10 08:35:32

59

Views

Check of Monotone Property

Published on 10 Jun 2017 - 8:35

score 67 · Answer 13 · 2017-06-13 06:19:08

67

Views

Given the monotone decreasing function and a point $a\in\mathbb{R}$ prove that f is continuous in a.

Published on 13 Jun 2017 - 6:19

score 2.1k · Answer 14 · 2017-06-25 00:09:41

2.1k

Views

Why is a strictly monotonic mapping between intervals continuous?

Published on 25 Jun 2017 - 0:09

score 855 · Answer 15 · 2017-06-27 16:36:05

855

Views

Bivariate function monotone in each variable $\Rightarrow$ continuous a.e.?

Published on 27 Jun 2017 - 16:36

List Question

$f'(x)\neq0 \Rightarrow$ f is monotonic

What is the exact limit of the following monotone sequence?

Increasing sequence of functions with subsequence that converges in $H^1$ and $L^2$; does the full sequence converge?

If $a<b$, the $\lim_{x\to a^+}f(x) \le \lim_{x\to b^-}f(x) $?

Prove that $(1+\frac{\log(x)}{x})^x$ is monotonically increasing function for $x \geq 1$

Is a quasiconvex function always the monotone image of a convex function?

Is every monotonic simple function a step function?

Doubt in discontinuities of a monotonic function.

Proof verification : $\lim_{x \to c^+}f(x)=\inf\{f(x): x>c\}$ for increasing $f$

Is the power of a positive strictly monotonic function convex/concave?

Proof verification : $f$ is continuous at $c$ $\Leftrightarrow$ $f$ has zero-jump at $c$ for increasing $f$

Check of Monotone Property

Given the monotone decreasing function and a point $a\in\mathbb{R}$ prove that f is continuous in a.

Why is a strictly monotonic mapping between intervals continuous?

Bivariate function monotone in each variable $\Rightarrow$ continuous a.e.?

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