Question

Polynomials in $y=e^x$ dense in C[1,e]

score 197 · Answer 1 · 2017-05-14 17:15:57

197

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Polynomials in $y=e^x$ dense in C[1,e]

Published on 14 May 2017 - 17:15

score 950 · Answer 2 · 2017-08-02 23:04:48

950

Views

Use Weierstrass Approximation to prove that $f(x)=0$. With questions on the detail.

Published on 02 Aug 2017 - 23:04

score 142 · Answer 3 · 2017-08-03 00:42:06

142

Views

Let $f:[0,1]\rightarrow\mathbb{R}$ be continuous such that $\int_0^1 x^{2k}f(x)dx=0$

Published on 03 Aug 2017 - 0:42

score 125 · Answer 4 · 2017-08-03 16:31:32

125

Views

Assume $f$ is continuous on $[-1,1]$. If $\int_{-1}^{1}f(x)x^ndx=0$, for all nonnegative integer $n$, can we prove that $f(x)=0$?

Published on 03 Aug 2017 - 16:31

score 162 · Answer 5 · 2017-08-03 17:52:56

162

Views

$\int_0^1 t^{n\lambda}f(t)dt=0$ for all but finitely many $n$

Published on 03 Aug 2017 - 17:52

score 470 · Answer 6 · 2017-08-07 17:40:35

470

Views

Use Stone-Weierstrass theorem to show that $f$ will be $0$ for all $x\in [0,1]$.

Published on 07 Aug 2017 - 17:40

score 203 · Answer 7 · 2017-08-07 18:20:37

203

Views

If $\int_0^1 f(x)x^{2n+1}dx=0$ for all but finitely many $n\in\mathbb{N}$, then $f=0$ on $[0,1]$.

Published on 07 Aug 2017 - 18:20

score 1.2k · Answer 8 · 2017-09-26 14:58:40

1.2k

Views

Show the existence of a sequence of polynomials that converges to $f$ on any compact subset of $\mathbb{R}$.

Published on 26 Sep 2017 - 14:58

score 139 · Answer 9 · 2017-09-26 16:43:52

139

Views

Prove $\exists$ a sequence of polynomials which converges to $f$ on any compact subset of $\mathbb{R}$.

Published on 26 Sep 2017 - 16:43

score 366 · Answer 10 · 2017-09-28 17:32:56

366

Views

Prove Weierstrass approximation theorem for 0.2(3)

Published on 28 Sep 2017 - 17:32

score 230 · Answer 11 · 2017-11-06 02:47:59

230

Views

Span$\{1,\sin t,\sin ^2t,\cdots\}$ is dense in $\mathscr{C}[0,1].$

Published on 06 Nov 2017 - 2:47

score 386 · Answer 12 · 2017-11-11 15:50:56

386

Views

A problem about the Weierstrass approximation theorem

Published on 11 Nov 2017 - 15:50

score 807 · Answer 13 · 2017-11-28 18:27:48

807

Views

Proving Peano's Existence Theorem by approximating with $C^{\infty}$ functions using Weierstrass' Theorem.

Published on 28 Nov 2017 - 18:27

score 33 · Answer 14 · 2017-11-29 04:55:08

33

Views

Question on a proof that involves continuity

Published on 29 Nov 2017 - 4:55

score 1.8k · Answer 15 · 2017-12-04 11:37:28

1.8k

Views

Proof of inequality in Weierstrass approximation theorem proof through probability

Published on 04 Dec 2017 - 11:37

List Question

Polynomials in $y=e^x$ dense in C[1,e]

Use Weierstrass Approximation to prove that $f(x)=0$. With questions on the detail.

Let $f:[0,1]\rightarrow\mathbb{R}$ be continuous such that $\int_0^1 x^{2k}f(x)dx=0$

Assume $f$ is continuous on $[-1,1]$. If $\int_{-1}^{1}f(x)x^ndx=0$, for all nonnegative integer $n$, can we prove that $f(x)=0$?

$\int_0^1 t^{n\lambda}f(t)dt=0$ for all but finitely many $n$

Use Stone-Weierstrass theorem to show that $f$ will be $0$ for all $x\in [0,1]$.

If $\int_0^1 f(x)x^{2n+1}dx=0$ for all but finitely many $n\in\mathbb{N}$, then $f=0$ on $[0,1]$.

Show the existence of a sequence of polynomials that converges to $f$ on any compact subset of $\mathbb{R}$.

Prove $\exists$ a sequence of polynomials which converges to $f$ on any compact subset of $\mathbb{R}$.

Prove Weierstrass approximation theorem for 0.2(3)

Span$\{1,\sin t,\sin ^2t,\cdots\}$ is dense in $\mathscr{C}[0,1].$

A problem about the Weierstrass approximation theorem

Proving Peano's Existence Theorem by approximating with $C^{\infty}$ functions using Weierstrass' Theorem.

Question on a proof that involves continuity

Proof of inequality in Weierstrass approximation theorem proof through probability

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