Question

Find the limit function $f$ of $\{F_n\}$. $F_n=nx^n(1-x^2) $

score 36 · Answer 1 · 2017-11-29 21:30:12

36

Views

Find the limit function $f$ of $\{F_n\}$. $F_n=nx^n(1-x^2) $

Published on 29 Nov 2017 - 21:30

score 470 · Answer 2 · 2017-11-29 21:55:37

470

Views

Find the limit function $f$ for $\{F_n\}$ where $F_n=nxe^{-nx^2}$

Published on 29 Nov 2017 - 21:55

score 183 · Answer 3 · 2026-02-25 07:11:03

183

Views

Does pointwise convergence of a sequence of functions in each closed subinterval of an open interval imply pointwise convergence in the open interval?

Published on 25 Feb 2026 - 7:11

score 48 · Answer 4 · 2017-11-30 15:54:18

Given $\{f_n\}$ uniformly bounded and $f_n \to f$ uniformly on $S.$ Prove $\frac{f_1 + f_2 + \cdots + f_n}{n} \to f$ uniformly on $S.$

score 63 · Answer 5 · 2017-12-01 16:34:05

63

Views

if $\{f_n\}$ converges point wise to $f$ on $[a,b]$. $f_n$ is nondecreasing for each n. Prove that $f$ is nondecresing.

Published on 01 Dec 2017 - 16:34

score 86 · Answer 6 · 2017-12-02 19:57:36

86

Views

Let $f_n$ converges uniformly to $f$ on $S$. Show: $\lim_{n\to \infty}||f_n||_S=||f||_S$.

Published on 02 Dec 2017 - 19:57

score 55 · Answer 7 · 2017-12-04 03:41:15

55

Views

Show that $\phi$ is nowhere differentiable in $\mathbb R$ if $\alpha \beta >1$.

Published on 04 Dec 2017 - 3:41

score 49 · Answer 8 · 2017-12-05 18:16:17

49

Views

limit function $f$ of $\{F_n\}$. $F_n=nx^n(1-x^2) $

Published on 05 Dec 2017 - 18:16

score 269 · Answer 9 · 2026-02-25 07:14:57

269

Views

Uniform convergence of a sequence of functions on $[0, 1]$

Published on 25 Feb 2026 - 7:14

score 43 · Answer 10 · 2026-02-25 07:13:24

43

Views

How can I prove $f=g$ when $f_k$ pointwisely converges to $f$, $L^2$ converges to $g$, and $f$, $g$ are continuous?

Published on 25 Feb 2026 - 7:13

score 60 · Answer 11 · 2017-12-08 09:41:21

60

Views

Uniform convergence of the sequence of function.

Published on 08 Dec 2017 - 9:41

score 1.3k · Answer 12 · 2017-12-08 10:18:36

1.3k

Views

Convergence of $F_n=x^n\sin(nx)$ on $S=(-1,1)$

Published on 08 Dec 2017 - 10:18

score 89 · Answer 13 · 2017-12-08 20:23:09

89

Views

Evaluate $\lim_{n\to\infty}\int^2_0\frac{dx}{1+x^{2n}}$

Published on 08 Dec 2017 - 20:23

score 144 · Answer 14 · 2017-12-09 11:34:14

144

Views

why is $f_{n}\rightarrow f \; \text{point-wise} \iff \limsup_{n\rightarrow\infty}f_{n}=\liminf_{n\rightarrow\infty}f_{n}=f$

Published on 09 Dec 2017 - 11:34

score 355 · Answer 15 · 2017-12-13 03:28:40

355

Views

A fixed point theorem for continuous and increasing function on $[0,1]$

Published on 13 Dec 2017 - 3:28

List Question

Find the limit function $f$ of $\{F_n\}$. $F_n=nx^n(1-x^2) $

Find the limit function $f$ for $\{F_n\}$ where $F_n=nxe^{-nx^2}$

Does pointwise convergence of a sequence of functions in each closed subinterval of an open interval imply pointwise convergence in the open interval?

Given $\{f_n\}$ uniformly bounded and $f_n \to f$ uniformly on $S.$ Prove $\frac{f_1 + f_2 + \cdots + f_n}{n} \to f$ uniformly on $S.$

if $\{f_n\}$ converges point wise to $f$ on $[a,b]$. $f_n$ is nondecreasing for each n. Prove that $f$ is nondecresing.

Let $f_n$ converges uniformly to $f$ on $S$. Show: $\lim_{n\to \infty}||f_n||_S=||f||_S$.

Show that $\phi$ is nowhere differentiable in $\mathbb R$ if $\alpha \beta >1$.

limit function $f$ of $\{F_n\}$. $F_n=nx^n(1-x^2) $

Uniform convergence of a sequence of functions on $[0, 1]$

How can I prove $f=g$ when $f_k$ pointwisely converges to $f$, $L^2$ converges to $g$, and $f$, $g$ are continuous?

Uniform convergence of the sequence of function.

Convergence of $F_n=x^n\sin(nx)$ on $S=(-1,1)$

Evaluate $\lim_{n\to\infty}\int^2_0\frac{dx}{1+x^{2n}}$

why is $f_{n}\rightarrow f \; \text{point-wise} \iff \limsup_{n\rightarrow\infty}f_{n}=\liminf_{n\rightarrow\infty}f_{n}=f$

A fixed point theorem for continuous and increasing function on $[0,1]$

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