Question

If $f$ is continuous on $[0,1]$ and if $\int\limits_{0}^{1} f(x) x^n dx = 0, (n=0,1,2,...)$, prove that $f(x)=0$ on $[0,1]$.

score 2.4k · Answer 1 · 2014-02-07 02:03:51

2.4k

Views

If $f$ is continuous on $[0,1]$ and if $\int\limits_{0}^{1} f(x) x^n dx = 0, (n=0,1,2,...)$, prove that $f(x)=0$ on $[0,1]$.

Published on 07 Feb 2014 - 2:03

score 120 · Answer 2 · 2014-02-10 09:10:14

120

Views

How do I show $x^\frac{1}{3}$ is uniformly continuous?

Published on 10 Feb 2014 - 9:10

score 99 · Answer 3 · 2014-02-11 16:41:14

99

Views

limit of continuous functions

Published on 11 Feb 2014 - 16:41

score 1.8k · Answer 4 · 2014-02-12 11:08:21

1.8k

Views

If $f,g$ are uniform continuous with $f$ bounded, then $fg$ is uniform continuous.

Published on 12 Feb 2014 - 11:08

score 1.3k · Answer 5 · 2014-02-18 16:32:29

1.3k

Views

Prove that the Rational function $f\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}$ is uniformly continuous

Published on 18 Feb 2014 - 16:32

score 3.6k · Answer 6 · 2014-02-20 14:51:07

3.6k

Views

A game with $\delta$, $\epsilon$ and uniform continuity.

Published on 20 Feb 2014 - 14:51

score 448 · Answer 7 · 2026-03-28 09:55:04

448

Views

Arzela Ascoli variation theorem

Published on 28 Mar 2026 - 9:55

score 58 · Answer 8 · 2014-02-25 14:32:11

58

Views

Uniform Continuity ? How can you tell?

Published on 25 Feb 2014 - 14:32

score 123 · Answer 9 · 2014-02-26 06:28:20

123

Views

Is this claim harder to prove for arbitrary metric spaces than for the reals?

Published on 26 Feb 2014 - 6:28

score 1.5k · Answer 10 · 2014-02-26 12:21:46

1.5k

Views

Show that there are $ a,b \geq 0 $ so that $ |f(x)| \leq ax+b, \forall x \geq 0.$

Published on 26 Feb 2014 - 12:21

score 4k · Answer 11 · 2014-02-28 00:25:36

4k

Views

Differentiable function with bounded derivative, yet not uniformly continuous

Published on 28 Feb 2014 - 0:25

score 51 · Answer 12 · 2014-03-06 11:38:28

51

Views

Can a Lipshitz Continuous function on an interval with a Uniformly continuous derivative have a nonexistant second derivative.

Published on 06 Mar 2014 - 11:38

score 4.6k · Answer 13 · 2014-03-09 22:57:50

4.6k

Views

A function vanishing at infinity is uniformly continuous

Published on 09 Mar 2014 - 22:57

score 187 · Answer 14 · 2014-03-11 14:00:18

187

Views

If f(x) is continuous, can it be uniformly continuous?

Published on 11 Mar 2014 - 14:00

score 1k · Answer 15 · 2017-04-11 13:05:26

1k

Views

$e^x \sin x$ Is not Uniformly Continuous

Published on 11 Apr 2017 - 13:05

List Question

If $f$ is continuous on $[0,1]$ and if $\int\limits_{0}^{1} f(x) x^n dx = 0, (n=0,1,2,...)$, prove that $f(x)=0$ on $[0,1]$.

How do I show $x^\frac{1}{3}$ is uniformly continuous?

limit of continuous functions

If $f,g$ are uniform continuous with $f$ bounded, then $fg$ is uniform continuous.

Prove that the Rational function $f\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}$ is uniformly continuous

A game with $\delta$, $\epsilon$ and uniform continuity.

Arzela Ascoli variation theorem

Uniform Continuity ? How can you tell?

Is this claim harder to prove for arbitrary metric spaces than for the reals?

Show that there are $ a,b \geq 0 $ so that $ |f(x)| \leq ax+b, \forall x \geq 0.$

Differentiable function with bounded derivative, yet not uniformly continuous

Can a Lipshitz Continuous function on an interval with a Uniformly continuous derivative have a nonexistant second derivative.

A function vanishing at infinity is uniformly continuous

If f(x) is continuous, can it be uniformly continuous?

$e^x \sin x$ Is not Uniformly Continuous

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