Question

Show that the directional derivatives of $f$ and $g$ exist everywhere, but that there is a $u \neq 0$ for which $h'(0,u)$ does not

score 450 · Answer 1 · 2026-03-24 23:58:04

450

Views

Show that the directional derivatives of $f$ and $g$ exist everywhere, but that there is a $u \neq 0$ for which $h'(0,u)$ does not

Published on 24 Mar 2026 - 23:58

score 103 · Answer 2 · 2026-04-14 22:00:33

103

Views

Let $C = \{\frac{a}{b}|a\in A, b\in B)$. Prove that $\sup C=\frac{\sup A}{\inf B}$

Published on 14 Apr 2026 - 22:00

score 204 · Answer 3 · 2026-04-17 23:19:49

204

Views

Angular values for input to a neural network

Published on 17 Apr 2026 - 23:19

score 57 · Answer 4 · 2026-04-12 23:02:19

57

Views

(Non) differentiability of a function in a point.

Published on 12 Apr 2026 - 23:02

score 755 · Answer 5 · 2026-04-10 01:21:21

755

Views

Every rearrangement of an absolutely convergent series converges to the same sum (Rudin)

Published on 10 Apr 2026 - 1:21

score 31 · Answer 6 · 2026-04-15 17:35:36

31

Views

Linear stability of fixed points of $N_{t+1}=\frac{aN_t}{(1+bN_t)^c}$

Published on 15 Apr 2026 - 17:35

score 42 · Answer 7 · 2026-04-16 09:21:56

42

Views

Given $\lim_{n\to \infty}\int_A(f_{n+1}-f_n)^2d\mu=0$ ,$ \int_Xf_n^2d\mu \le k $, is {$f_n $} uniformly integrable on $A$?

Published on 16 Apr 2026 - 9:21

score 386 · Answer 8 · 2026-03-26 22:24:11

386

Views

Showing that a Hilbert space is finite dimensional

Published on 26 Mar 2026 - 22:24

score 158 · Answer 9 · 2026-04-11 18:52:19

158

Views

If a function preserves integrability, must it have linear growth?

Published on 11 Apr 2026 - 18:52

score 57 · Answer 10 · 2026-04-16 09:20:32

57

Views

Where is the error in this proof for showing that $f:\mathbb{R}\rightarrow\mathbb{R},x\mapsto\sin{(2\pi x)}$ is constant?

Published on 16 Apr 2026 - 9:20

score 981 · Answer 11 · 2026-04-17 10:27:26

981

Views

Show continuously differentiable image of Jordan measurable set is Jordan measurable

Published on 17 Apr 2026 - 10:27

score 264 · Answer 12 · 2026-04-16 07:12:33

264

Views

Showing that $\sum_{j=0}^{2n-1}{\cos^n(\frac{j\pi}{2n})(2\cos(\frac{2j\pi}n)+1)\cos(\frac{j\pi}2-\frac{2j\pi}n)}$ is never an integer for $n>10$

Published on 16 Apr 2026 - 7:12

score 209 · Answer 13 · 2026-04-16 13:25:18

209

Views

Is this true: $\lim_{x\to 0} \frac{1-(\cos x)^n}{x^2}=\frac n2$

Published on 16 Apr 2026 - 13:25

score 309 · Answer 14 · 2026-04-11 04:39:14

309

Views

Proof verification: a function with finitely many points of discontinuity is Riemann integrable

Published on 11 Apr 2026 - 4:39

score 345 · Answer 15 · 2026-04-13 02:17:03

345

Views

Asymptotics of a recursive sequence

Published on 13 Apr 2026 - 2:17

List Question

Show that the directional derivatives of $f$ and $g$ exist everywhere, but that there is a $u \neq 0$ for which $h'(0,u)$ does not

Let $C = \{\frac{a}{b}|a\in A, b\in B)$. Prove that $\sup C=\frac{\sup A}{\inf B}$

Angular values for input to a neural network

(Non) differentiability of a function in a point.

Every rearrangement of an absolutely convergent series converges to the same sum (Rudin)

Linear stability of fixed points of $N_{t+1}=\frac{aN_t}{(1+bN_t)^c}$

Given $\lim_{n\to \infty}\int_A(f_{n+1}-f_n)^2d\mu=0$ ,$ \int_Xf_n^2d\mu \le k $, is {$f_n $} uniformly integrable on $A$?

Showing that a Hilbert space is finite dimensional

If a function preserves integrability, must it have linear growth?

Where is the error in this proof for showing that $f:\mathbb{R}\rightarrow\mathbb{R},x\mapsto\sin{(2\pi x)}$ is constant?

Show continuously differentiable image of Jordan measurable set is Jordan measurable

Showing that $\sum_{j=0}^{2n-1}{\cos^n(\frac{j\pi}{2n})(2\cos(\frac{2j\pi}n)+1)\cos(\frac{j\pi}2-\frac{2j\pi}n)}$ is never an integer for $n>10$

Is this true: $\lim_{x\to 0} \frac{1-(\cos x)^n}{x^2}=\frac n2$

Proof verification: a function with finitely many points of discontinuity is Riemann integrable

Asymptotics of a recursive sequence

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