Question

How to understand whether Weierstrass $M$ test is applicable or not.

score 148 · Answer 1 · 2019-12-04 14:54:14

148

Views

How to understand whether Weierstrass $M$ test is applicable or not.

Published on 04 Dec 2019 - 14:54

score 43 · Answer 2 · 2019-12-04 15:20:29

43

Views

$f_n, f$ RI and continuous and $\int|f_n(x)-f(x)|dx \to 0$ as $n \to \infty$ implies $f_n \to f$ uniformly

Published on 04 Dec 2019 - 15:20

score 1.2k · Answer 3 · 2019-12-04 15:22:12

1.2k

Views

Can Abel's test and Dirichlet test be used interchangably?

Published on 04 Dec 2019 - 15:22

score 85 · Answer 4 · 2019-12-04 18:05:04

85

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Uniform convergence of $f_n(x) := \frac{1}{1+n^2x^2}$ and $f_n(x) := \sum_{k=0}^n \frac{(x \sin x)^k}{k!}$

Published on 04 Dec 2019 - 18:05

score 478 · Answer 5 · 2026-03-30 13:59:13

478

Views

Proof $\frac{1}{f_n}$ converges uniformly towards $\frac{1}{f}$

Published on 30 Mar 2026 - 13:59

score 48 · Answer 6 · 2019-12-05 04:21:13

48

Views

Give an example of a function that converges to its Taylor series for $x\geq 0$ but not for $x<0$.

Published on 05 Dec 2019 - 4:21

score 695 · Answer 7 · 2026-02-23 02:55:23

695

Views

A sequence of polynomials converging pointwise to a given continuous function on $\mathbb R$ convergence being uniform in every compact interval.

Published on 23 Feb 2026 - 2:55

score 155 · Answer 8 · 2026-02-23 03:00:00

155

Views

Find a sequence of functions ${p_n}$ which converges uniformly to $f$ on $[0,1]$ with $p_n(0)=p_n(1)=0.$

Published on 23 Feb 2026 - 3:00

score 51 · Answer 9 · 2019-12-07 14:12:51

51

Views

is $x^n$ uniformly convergence on $[0,1)$

Published on 07 Dec 2019 - 14:12

score 34 · Answer 10 · 2019-12-08 01:22:19

34

Views

Let $d(x)=min_{n \in \mathbb Z}|x-n|$, Prove that $f(x)=\sum_{n=1}^{\infty} \frac{d(10^{n}x)}{10^{n}}$ is a continuous function on $\mathbb R$.

Published on 08 Dec 2019 - 1:22

score 43 · Answer 11 · 2019-12-08 02:20:24

43

Views

Pointwise Convergence but not Uniform Convergence

Published on 08 Dec 2019 - 2:20

score 27 · Answer 12 · 2026-02-24 05:30:51

27

Views

Sequences and uniform convergence

Published on 24 Feb 2026 - 5:30

score 74 · Answer 13 · 2019-12-09 00:45:08

74

Views

Question on Uniform Convergence of a Sum

Published on 09 Dec 2019 - 0:45

score 484 · Answer 14 · 2026-02-23 23:09:20

484

Views

Find the pointwise limit and the uniform convergence of $f_n(x) = x(1-x^n)$ and $f_n(x) = \frac{nx}{n+2}$

Published on 23 Feb 2026 - 23:09

score 66 · Answer 15 · 2019-12-09 15:00:27

66

Views

Convergence of sequences in $l^{\infty}$

Published on 09 Dec 2019 - 15:00

List Question

How to understand whether Weierstrass $M$ test is applicable or not.

$f_n, f$ RI and continuous and $\int|f_n(x)-f(x)|dx \to 0$ as $n \to \infty$ implies $f_n \to f$ uniformly

Can Abel's test and Dirichlet test be used interchangably?

Uniform convergence of $f_n(x) := \frac{1}{1+n^2x^2}$ and $f_n(x) := \sum_{k=0}^n \frac{(x \sin x)^k}{k!}$

Proof $\frac{1}{f_n}$ converges uniformly towards $\frac{1}{f}$

Give an example of a function that converges to its Taylor series for $x\geq 0$ but not for $x<0$.

A sequence of polynomials converging pointwise to a given continuous function on $\mathbb R$ convergence being uniform in every compact interval.

Find a sequence of functions ${p_n}$ which converges uniformly to $f$ on $[0,1]$ with $p_n(0)=p_n(1)=0.$

is $x^n$ uniformly convergence on $[0,1)$

Let $d(x)=min_{n \in \mathbb Z}|x-n|$, Prove that $f(x)=\sum_{n=1}^{\infty} \frac{d(10^{n}x)}{10^{n}}$ is a continuous function on $\mathbb R$.

Pointwise Convergence but not Uniform Convergence

Sequences and uniform convergence

Question on Uniform Convergence of a Sum

Find the pointwise limit and the uniform convergence of $f_n(x) = x(1-x^n)$ and $f_n(x) = \frac{nx}{n+2}$

Convergence of sequences in $l^{\infty}$

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