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Proving $u_n(x)\le v_n(x), \sum\limits_{n=1}^{\infty}v_n(x)\to f$ uniformlly $\Longrightarrow\sum\limits_{n=1}^{\infty}u_n(x)\to g$ uniformly

score 81 · Answer 1 · 2026-04-14 23:45:29

81

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Proving $u_n(x)\le v_n(x), \sum\limits_{n=1}^{\infty}v_n(x)\to f$ uniformlly $\Longrightarrow\sum\limits_{n=1}^{\infty}u_n(x)\to g$ uniformly

Published on 14 Apr 2026 - 23:45

score 200 · Answer 2 · 2026-04-16 05:40:01

200

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Calculating radius for $\sum\frac{\sin{n^3x}}{n^2}$

Published on 16 Apr 2026 - 5:40

score 4k · Answer 3 · 2026-04-15 23:19:35

4k

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If $f_n\to f$ uniformly on [a,b] and f is continious on [a,b] then $f_n$ is continious in [a,b]

Published on 15 Apr 2026 - 23:19

score 586 · Answer 4 · 2026-04-17 02:44:14

586

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Prove that $f_n(x) = 1 - \cos(\frac{x}{n})$ is uniformly convergent

Published on 17 Apr 2026 - 2:44

score 176 · Answer 5 · 2026-04-16 15:54:31

176

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If $\lim_{x\to\infty}u_k(x) = b_k$, how can we show $\lim_{x\to\infty}\sum_0^\infty u_k(x)=\sum_{0}^\infty b_k$?

Published on 16 Apr 2026 - 15:54

score 112 · Answer 6 · 2026-04-15 14:59:07

112

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Check the continuity of the next function $f(x)=\sum_{n=1}^{\infty}(x+\frac{1}{n^2})^n$

Published on 15 Apr 2026 - 14:59

score 101 · Answer 7 · 2026-04-16 00:06:36

101

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Does $\lim_{t\to 0}\frac{x \sin(xt)}{1+x^2}=0$ uniformly over $x\in \mathbb{R}$?

Published on 16 Apr 2026 - 0:06

score 190 · Answer 8 · 2026-04-17 14:40:50

190

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$F(u)= \frac{2}{\pi}\int_{0}^\infty \frac{uf(x)}{u^2 + x^2}dx.$ Show that $\lim\limits_{u\downarrow0}F(u)=f(0)$.

Published on 17 Apr 2026 - 14:40

score 844 · Answer 9 · 2026-04-14 12:48:38

844

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How to Prove that if $\sum_{k=0}^{\infty}a_k$ converges, $\sum_{k=0}^{\infty}{a_k}{x^k}$ converges uniformly on $[0, 1]$.

Published on 14 Apr 2026 - 12:48

score 413 · Answer 10 · 2026-04-15 18:33:23

413

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Show that $\int_0^\infty e^{-(x-u/x)^2}(1-\frac{u}{x^2})dx$ converges uniformly on $u\in [\delta,L]$

Published on 15 Apr 2026 - 18:33

score 70 · Answer 11 · 2026-04-14 20:18:53

70

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Is $\lim_{t\to 0}\frac{e^{xt}-1}{x}=0$ uniformly on $x>0$?

Published on 14 Apr 2026 - 20:18

score 1k · Answer 12 · 2026-04-15 22:45:23

1k

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Weighted uniform convergence of Taylor series of exponential function

Published on 15 Apr 2026 - 22:45

score 1.8k · Answer 13 · 2026-04-16 21:06:57

1.8k

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Proving Uniform Convergence

Published on 16 Apr 2026 - 21:06

score 181 · Answer 14 · 2026-04-16 23:24:28

181

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Proving uniform convergence of a sequence

Published on 16 Apr 2026 - 23:24

score 87 · Answer 15 · 2026-04-16 20:03:57

87

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Proving Uniform Convergence of a Sequence3

Published on 16 Apr 2026 - 20:03

List Question

Proving $u_n(x)\le v_n(x), \sum\limits_{n=1}^{\infty}v_n(x)\to f$ uniformlly $\Longrightarrow\sum\limits_{n=1}^{\infty}u_n(x)\to g$ uniformly

Calculating radius for $\sum\frac{\sin{n^3x}}{n^2}$

If $f_n\to f$ uniformly on [a,b] and f is continious on [a,b] then $f_n$ is continious in [a,b]

Prove that $f_n(x) = 1 - \cos(\frac{x}{n})$ is uniformly convergent

If $\lim_{x\to\infty}u_k(x) = b_k$, how can we show $\lim_{x\to\infty}\sum_0^\infty u_k(x)=\sum_{0}^\infty b_k$?

Check the continuity of the next function $f(x)=\sum_{n=1}^{\infty}(x+\frac{1}{n^2})^n$

Does $\lim_{t\to 0}\frac{x \sin(xt)}{1+x^2}=0$ uniformly over $x\in \mathbb{R}$?

$F(u)= \frac{2}{\pi}\int_{0}^\infty \frac{uf(x)}{u^2 + x^2}dx.$ Show that $\lim\limits_{u\downarrow0}F(u)=f(0)$.

How to Prove that if $\sum_{k=0}^{\infty}a_k$ converges, $\sum_{k=0}^{\infty}{a_k}{x^k}$ converges uniformly on $[0, 1]$.

Show that $\int_0^\infty e^{-(x-u/x)^2}(1-\frac{u}{x^2})dx$ converges uniformly on $u\in [\delta,L]$

Is $\lim_{t\to 0}\frac{e^{xt}-1}{x}=0$ uniformly on $x>0$?

Weighted uniform convergence of Taylor series of exponential function

Proving Uniform Convergence

Proving uniform convergence of a sequence

Proving Uniform Convergence of a Sequence3

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