Question

If $f:[a, b] \to \mathbb{R}$ is a continuous function, s.t. $f(x)>0$ for all $x$, prove that there exists $c >0$, s.t. $f(x) > c$ for all $x$.

score 235 · Answer 1 · 2026-05-15 07:41:52

If $f:[a, b] \to \mathbb{R}$ is a continuous function, s.t. $f(x)>0$ for all $x$, prove that there exists $c >0$, s.t. $f(x) > c$ for all $x$.

score 17 · Answer 2 · 2026-04-15 02:29:41

17

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Characterization of non uniformly b0unded sequence of functions

Published on 15 Apr 2026 - 2:29

score 43 · Answer 3 · 2026-04-14 20:22:42

43

Views

Prove that if $f^{-1}(F)\in\mathcal{A}$ for all $F\in\mathcal{F}$, then $f$ is measurable.

Published on 14 Apr 2026 - 20:22

score 89 · Answer 4 · 2026-05-10 14:48:34

89

Views

About an estimate involving Sobolev norm for a $C^{1,1}$ function

Published on 10 May 2026 - 14:48

score 34 · Answer 5 · 2026-04-12 03:33:32

34

Views

Chain rule in multi dimensional case?

Published on 12 Apr 2026 - 3:33

score 565 · Answer 6 · 2026-04-11 20:25:07

565

Views

every open set in the extended real line ($\overline{\mathbb R}$) is a countable union of segments

Published on 11 Apr 2026 - 20:25

score 205 · Answer 7 · 2026-04-16 08:53:25

205

Views

Let $ f:(-1,1)\to(-1,1)$ be continuous, $f(x)=f(x^2)$ for every $x$ then the value of $f(\frac 1 4)$

Published on 16 Apr 2026 - 8:53

score 51 · Answer 8 · 2026-04-16 09:18:49

51

Views

Qualitative graph for a function of $x^{3}$.

Published on 16 Apr 2026 - 9:18

score 357 · Answer 9 · 2026-04-12 18:28:28

357

Views

Solving Riccati differential equation

Published on 12 Apr 2026 - 18:28

score 66 · Answer 10 · 2026-05-15 07:39:56

66

Views

Existence of another critical point

Published on 15 May 2026 - 7:39

score 32 · Answer 11 · 2026-04-16 08:23:06

32

Views

A confusion in checking differentiability at a point x=1. Cannot find what to write in place of $f(1-h)$ or $f(1+h)$

Published on 16 Apr 2026 - 8:23

score 1.1k · Answer 12 · 2026-05-10 16:13:14

1.1k

Views

zero sets of real analytic functions of several variables

Published on 10 May 2026 - 16:13

score 86 · Answer 13 · 2026-05-04 03:57:26

86

Views

Justify an approximation of $\sum_{n=1}^\infty|G_n|\log\left(\frac{n+1}{n}\right)$, where $G_n$ is the $n$th Gregory coefficient

Published on 04 May 2026 - 3:57

score 131 · Answer 14 · 2026-05-15 07:39:33

131

Views

Existence of a critical point between two local minimum

Published on 15 May 2026 - 7:39

score 78 · Answer 15 · 2026-05-15 16:52:06

78

Views

If $g(x) = \sup_{z \in [x, b]} f(z)$ is a concave function then $f(x)$ is also concave

Published on 15 May 2026 - 16:52

List Question

If $f:[a, b] \to \mathbb{R}$ is a continuous function, s.t. $f(x)>0$ for all $x$, prove that there exists $c >0$, s.t. $f(x) > c$ for all $x$.

Characterization of non uniformly b0unded sequence of functions

Prove that if $f^{-1}(F)\in\mathcal{A}$ for all $F\in\mathcal{F}$, then $f$ is measurable.

About an estimate involving Sobolev norm for a $C^{1,1}$ function

Chain rule in multi dimensional case?

every open set in the extended real line ($\overline{\mathbb R}$) is a countable union of segments

Let $ f:(-1,1)\to(-1,1)$ be continuous, $f(x)=f(x^2)$ for every $x$ then the value of $f(\frac 1 4)$

Qualitative graph for a function of $x^{3}$.

Solving Riccati differential equation

Existence of another critical point

A confusion in checking differentiability at a point x=1. Cannot find what to write in place of $f(1-h)$ or $f(1+h)$

zero sets of real analytic functions of several variables

Justify an approximation of $\sum_{n=1}^\infty|G_n|\log\left(\frac{n+1}{n}\right)$, where $G_n$ is the $n$th Gregory coefficient

Existence of a critical point between two local minimum

If $g(x) = \sup_{z \in [x, b]} f(z)$ is a concave function then $f(x)$ is also concave

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