List questions from uniform-convergence

Published on 30 Mar 2026 - 9:48

465

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Show that the series $\sum 3^n \sin(\frac{1}{4^n} x)$ converges absolutely and uniformly on $(a,\infty)$, where $a>0$.

Published on 12 May 2020 - 13:20

197

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Proving that $\lim\limits_{n \rightarrow \infty} \int^b_a f_n = \int^b_a f$

Published on 30 Mar 2026 - 9:50

49

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Evaluating a Limit by Applying a Proven Result

Published on 12 May 2020 - 20:44

82

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How to show an infinite series is $C^\infty$ - smooth

Published on 12 May 2020 - 21:51

110

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Determining if a function is differentiable

Published on 13 May 2020 - 2:42

184

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Prove or disprove uniform convergence

Published on 13 May 2020 - 11:51

34

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Convergence of specific power series

Published on 24 Feb 2026 - 7:04

18

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Convergence of a specific power series

Published on 13 May 2020 - 18:30

158

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uniform and absolute convergence of $\sum _{n=1}^{\infty }\:\frac{x^n}{1+x^n}$

Published on 24 Feb 2026 - 14:28

216

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How do we prove that uniform convergence preserves continuity?

Published on 14 May 2020 - 0:11

147

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How do we prove that uniform convergence preserves boundedness?

Published on 26 Mar 2026 - 14:18

46

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Show that the series $\sum_{n=1}^\infty \frac{1}{n} \frac{1}{(2+x^2)^n}$ converges uniformly for all $x \in \mathbb{R}$

Published on 14 May 2020 - 13:00

633

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Does $\sum_{n=1}^{\infty} a_n$ is absolutely convergent $\Rightarrow$ $\sum_{n=1}^{\infty} a_n\sin(nx)$ is absolutely and uniformly convergent?

Published on 26 Mar 2026 - 11:01

75

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Weierstrass-M test find $a_n$

Published on 06 Apr 2026 - 0:25

List Question

Compute the limit of a bounded integral by checking for uniform convergence

Show that the series $\sum 3^n \sin(\frac{1}{4^n} x)$ converges absolutely and uniformly on $(a,\infty)$, where $a>0$.

Proving that $\lim\limits_{n \rightarrow \infty} \int^b_a f_n = \int^b_a f$

Evaluating a Limit by Applying a Proven Result

How to show an infinite series is $C^\infty$ - smooth

Determining if a function is differentiable

Prove or disprove uniform convergence

Convergence of specific power series

Convergence of a specific power series

uniform and absolute convergence of $\sum _{n=1}^{\infty }\:\frac{x^n}{1+x^n}$

How do we prove that uniform convergence preserves continuity?

How do we prove that uniform convergence preserves boundedness?

Show that the series $\sum_{n=1}^\infty \frac{1}{n} \frac{1}{(2+x^2)^n}$ converges uniformly for all $x \in \mathbb{R}$

Does $\sum_{n=1}^{\infty} a_n$ is absolutely convergent $\Rightarrow$ $\sum_{n=1}^{\infty} a_n\sin(nx)$ is absolutely and uniformly convergent?

Weierstrass-M test find $a_n$

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