Question

Differentiability Implies Continuity Twist

score 60 · Answer 1 · 2026-04-13 07:04:05

60

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Differentiability Implies Continuity Twist

Published on 13 Apr 2026 - 7:04

score 152 · Answer 2 · 2026-04-06 17:32:52

152

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Find $f(x)$ if $f\left(\frac{x+y}{3}\right)=\frac{2+f(x)+f(y)}{3}$

Published on 06 Apr 2026 - 17:32

score 505 · Answer 3 · 2026-04-01 05:06:43

505

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If $L$ is a limit point of the sequence $(x^{(n)})^∞_{n=m}$, then $L$ is an adherent point of the set $\{x^{(n)}:n\ge m\}$.

Published on 01 Apr 2026 - 5:06

score 86 · Answer 4 · 2026-03-27 07:31:12

86

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$E=\left\{ \frac{n}{n+1}:n\in\mathbb{N}\right\} $and $F=\left\{ \frac{1}{1-x}:0\leq x<1\right\} $ is open or closed?

Published on 27 Mar 2026 - 7:31

score 100 · Answer 5 · 2026-04-06 21:21:27

100

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When can one write $f(x,y)$ as $|g(x)-g(y)|_2^2$ for some $g(\cdot)$?

Published on 06 Apr 2026 - 21:21

score 57 · Answer 6 · 2026-03-25 01:20:40

57

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If the power series$\sum_{n=1}^{\infty}a_{n}x^{n}$converges For $x=3$,Then

Published on 25 Mar 2026 - 1:20

score 607 · Answer 7 · 2026-04-12 06:29:58

607

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Is function is uniformly continuous on $\mathbb{R}$ then it is uniformly continuous on subset of $\mathbb{R}$?

Published on 12 Apr 2026 - 6:29

score 729 · Answer 8 · 2026-04-09 00:27:46

729

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Optimization problem "change of variables" injectivity requirement

Published on 09 Apr 2026 - 0:27

score 668 · Answer 9 · 2026-04-12 20:45:48

668

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How to prove $\lim \limits_{x \to 1^-} \sum\limits_{n=0}^\infty (-1)^nx^{n^2} = \frac{1}{2} \ $?

Published on 12 Apr 2026 - 20:45

score 68 · Answer 10 · 2026-04-06 12:39:57

68

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limit of $a_n = \left( \frac{ \sqrt{k} - 1 }{ \sqrt{k} + 1} \right )^n, \quad k\in \mathbb{N}$

Published on 06 Apr 2026 - 12:39

score 279 · Answer 11 · 2026-04-13 06:40:43

279

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Justifying connection between convergence of Fourier transform and Fourier Series for $L^2$ function

Published on 13 Apr 2026 - 6:40

score 147 · Answer 12 · 2026-03-25 04:40:56

147

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convergence of $ \sum_{k=1}^{\infty}{ \frac{1}{\sqrt{k(k+1)}} } $

Published on 25 Mar 2026 - 4:40

score 45 · Answer 13 · 2026-04-10 17:40:58

45

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Analysis: Finding the derivative of a two variable function.

Published on 10 Apr 2026 - 17:40

score 867 · Answer 14 · 2026-04-12 04:18:04

867

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Show the equivalence of arc length definitions

Published on 12 Apr 2026 - 4:18

score 143 · Answer 15 · 2018-01-25 11:33:36

To prove or disprove existence of a continuous function $f$ on $\mathbb R$ satisfying $f(x)\in\mathbb Q$ iff $f(x+1)\in\mathbb R\setminus\mathbb Q$

List Question

Differentiability Implies Continuity Twist

Find $f(x)$ if $f\left(\frac{x+y}{3}\right)=\frac{2+f(x)+f(y)}{3}$

If $L$ is a limit point of the sequence $(x^{(n)})^∞_{n=m}$, then $L$ is an adherent point of the set $\{x^{(n)}:n\ge m\}$.

$E=\left\{ \frac{n}{n+1}:n\in\mathbb{N}\right\} $and $F=\left\{ \frac{1}{1-x}:0\leq x<1\right\} $ is open or closed?

When can one write $f(x,y)$ as $|g(x)-g(y)|_2^2$ for some $g(\cdot)$?

If the power series$\sum_{n=1}^{\infty}a_{n}x^{n}$converges For $x=3$,Then

Is function is uniformly continuous on $\mathbb{R}$ then it is uniformly continuous on subset of $\mathbb{R}$?

Optimization problem "change of variables" injectivity requirement

How to prove $\lim \limits_{x \to 1^-} \sum\limits_{n=0}^\infty (-1)^nx^{n^2} = \frac{1}{2} \ $?

limit of $a_n = \left( \frac{ \sqrt{k} - 1 }{ \sqrt{k} + 1} \right )^n, \quad k\in \mathbb{N}$

Justifying connection between convergence of Fourier transform and Fourier Series for $L^2$ function

convergence of $ \sum_{k=1}^{\infty}{ \frac{1}{\sqrt{k(k+1)}} } $

Analysis: Finding the derivative of a two variable function.

Show the equivalence of arc length definitions

To prove or disprove existence of a continuous function $f$ on $\mathbb R$ satisfying $f(x)\in\mathbb Q$ iff $f(x+1)\in\mathbb R\setminus\mathbb Q$

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