Question

Calculating $\int_{0}^{\infty}e^{-x^{2}}$, motivation behind the defined function

score 94 · Answer 1 · 2026-04-12 21:22:59

94

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Calculating $\int_{0}^{\infty}e^{-x^{2}}$, motivation behind the defined function

Published on 12 Apr 2026 - 21:22

score 48 · Answer 2 · 2026-04-11 17:19:49

48

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Plausible conditions for the elements of a sequence of functions to become monotone given convergence to a monotone function

Published on 11 Apr 2026 - 17:19

score 74 · Answer 3 · 2026-04-13 20:07:40

74

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Uniform convergence on sequence of contractions composition

Published on 13 Apr 2026 - 20:07

score 221 · Answer 4 · 2026-04-15 22:11:45

221

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Evaluate $\lim_{n \rightarrow \infty} \int_{0}^{\pi} \frac{\sin(nx)}{nx}dx$. Explanation of certain steps in procedure.

Published on 15 Apr 2026 - 22:11

score 289 · Answer 5 · 2026-04-14 01:21:25

289

Views

Topology of uniform convergence on $C(X,Y)$ is independent of metric for compact $X$

Published on 14 Apr 2026 - 1:21

score 149 · Answer 6 · 2026-04-17 00:49:16

149

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Suppose $g \in C([0,1])$ and $f_{n}$ is a sequence in $C([0,1])$ that converges uniformly to $f$. Prove the equality

Published on 17 Apr 2026 - 0:49

score 317 · Answer 7 · 2026-04-17 06:25:46

317

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Show $\sum_{k = 1}^{\infty}x^{k}e^{-kx}$ converges uniformly in $[0,A]$

Published on 17 Apr 2026 - 6:25

score 94 · Answer 8 · 2026-04-10 22:40:28

94

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How to use Dirichlet/Abel test to prove the series is not uniform convergent

Published on 10 Apr 2026 - 22:40

score 297 · Answer 9 · 2026-04-11 10:28:59

297

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Differentiability of $\sum_{k=0}^{\infty}c_{k}e^{ikt}$ given $\lim_{k\to\infty}k^{m}c_{k}=0$

Published on 11 Apr 2026 - 10:28

score 82 · Answer 10 · 2026-04-14 03:25:31

82

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Determine if $\sum_{n = 1}^{\infty} \frac{1}{x^{2} + n^{2}}$ converges on $\mathbb{R}$. Proof verification

Published on 14 Apr 2026 - 3:25

score 70 · Answer 11 · 2026-04-16 18:54:36

70

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Evaluate $\sum_{n = 0}^{\infty}\frac{x^{2}}{(1+x^{2})^{n}}$

Published on 16 Apr 2026 - 18:54

score 77 · Answer 12 · 2026-04-14 06:57:18

77

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Convergence of a series of functions. Notation/ idea

Published on 14 Apr 2026 - 6:57

score 166 · Answer 13 · 2026-03-30 22:59:53

166

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Using Stirling's Formula to approximate radius of convergence of $\sum_{k = 0}^{\infty} \frac{x^k}{k!}$

Published on 30 Mar 2026 - 22:59

score 78 · Answer 14 · 2026-04-16 12:37:01

78

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Determine Radius of convergence of $\sum_{k = 1}^{\infty} \frac{k!}{k^{k}}x^{k}$

Published on 16 Apr 2026 - 12:37

score 45 · Answer 15 · 2026-04-14 12:26:16

45

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Compute $f(x) = \sum_{k = 1}^{\infty} \Bigg(\frac{1}{(k-1)!} + k\Bigg)x^{k-1}$

Published on 14 Apr 2026 - 12:26

List Question

Calculating $\int_{0}^{\infty}e^{-x^{2}}$, motivation behind the defined function

Plausible conditions for the elements of a sequence of functions to become monotone given convergence to a monotone function

Uniform convergence on sequence of contractions composition

Evaluate $\lim_{n \rightarrow \infty} \int_{0}^{\pi} \frac{\sin(nx)}{nx}dx$. Explanation of certain steps in procedure.

Topology of uniform convergence on $C(X,Y)$ is independent of metric for compact $X$

Suppose $g \in C([0,1])$ and $f_{n}$ is a sequence in $C([0,1])$ that converges uniformly to $f$. Prove the equality

Show $\sum_{k = 1}^{\infty}x^{k}e^{-kx}$ converges uniformly in $[0,A]$

How to use Dirichlet/Abel test to prove the series is not uniform convergent

Differentiability of $\sum_{k=0}^{\infty}c_{k}e^{ikt}$ given $\lim_{k\to\infty}k^{m}c_{k}=0$

Determine if $\sum_{n = 1}^{\infty} \frac{1}{x^{2} + n^{2}}$ converges on $\mathbb{R}$. Proof verification

Evaluate $\sum_{n = 0}^{\infty}\frac{x^{2}}{(1+x^{2})^{n}}$

Convergence of a series of functions. Notation/ idea

Using Stirling's Formula to approximate radius of convergence of $\sum_{k = 0}^{\infty} \frac{x^k}{k!}$

Determine Radius of convergence of $\sum_{k = 1}^{\infty} \frac{k!}{k^{k}}x^{k}$

Compute $f(x) = \sum_{k = 1}^{\infty} \Bigg(\frac{1}{(k-1)!} + k\Bigg)x^{k-1}$

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