Question

Show that $f$ is not differentiable at $(0,0)$, despite being differentiable in every direction $v\in\textbf{R}^{2}$ at $(0,0)$.

score 223 · Answer 1 · 2026-04-13 06:48:49

223

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Show that $f$ is not differentiable at $(0,0)$, despite being differentiable in every direction $v\in\textbf{R}^{2}$ at $(0,0)$.

Published on 13 Apr 2026 - 6:48

score 1k · Answer 2 · 2026-04-09 23:12:45

1k

Views

Mapping between a set and its power set

Published on 09 Apr 2026 - 23:12

score 238 · Answer 3 · 2026-04-16 16:58:09

238

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Let $A,B,X$ be sets such that $A\cup B = X$ and $A \cap B = ∅$. Show that $A = X\backslash B$ and $B = X\backslash A$.

Published on 16 Apr 2026 - 16:58

score 51 · Answer 4 · 2026-04-16 08:30:35

51

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If we have $f : x→ y$ with $S \subset x$ what can we say about $f^{-1}f(S)$ and $S$

Published on 16 Apr 2026 - 8:30

score 130 · Answer 5 · 2026-04-16 01:18:28

130

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Find $\sup\left\{ \frac{m}{|m| + n }\right\} $ where $m \in \Bbb{Z}$ and $n \in \Bbb{N}$

Published on 16 Apr 2026 - 1:18

score 58 · Answer 6 · 2026-04-17 04:42:48

58

Views

Find Taylor serie and radius of convergence

Published on 17 Apr 2026 - 4:42

score 25 · Answer 7 · 2026-04-14 16:47:15

A theory $T$ with only finitely many complete extensions is finitely axiomatizable iff each complete extension of $T$ is finitely axiomatizable

score 40 · Answer 8 · 2026-04-13 07:47:40

40

Views

Obtaining condition for existence of two Chords through a single point with their Mid-points on the $x$-Axis

Published on 13 Apr 2026 - 7:47

score 154 · Answer 9 · 2026-04-16 14:48:45

154

Views

Let $f:[a,b]\to\Bbb R$ be continuous and take any $\epsilon>0$ . Construct a step function $T$ on $[a.b]$ with..

Published on 16 Apr 2026 - 14:48

score 320 · Answer 10 · 2026-04-12 14:34:18

320

Views

Proof for uniform convergence of sequence of functions

Published on 12 Apr 2026 - 14:34

score 33 · Answer 11 · 2026-04-15 09:12:05

33

Views

If there is a sequence of structures which are in $K=\text{Mod}(\Phi),\Phi\subseteq FO(\tau)$ then $\mathfrak{B}\in \mathcal{K}$

Published on 15 Apr 2026 - 9:12

score 62 · Answer 12 · 2026-04-16 08:43:36

62

Views

Check the uniform convergence of $ \sum\limits_{k=1}^{\infty} \left ( \frac{x \sin x}{1+x} \right )^k$ where $x \in [0,1]$

Published on 16 Apr 2026 - 8:43

score 109 · Answer 13 · 2026-04-15 09:54:50

109

Views

What English sentences are represented by following expressions?

Published on 15 Apr 2026 - 9:54

score 82 · Answer 14 · 2026-04-15 22:43:44

82

Views

For angles $A$ and $B$ in a triangle, is $\cos\frac B2-\cos \frac A2=\cos B-\cos A$ enough to conclude that $A=B$?

Published on 15 Apr 2026 - 22:43

score 53 · Answer 15 · 2026-04-14 09:47:03

53

Views

Limit, supremum and sets

Published on 14 Apr 2026 - 9:47

List Question

Show that $f$ is not differentiable at $(0,0)$, despite being differentiable in every direction $v\in\textbf{R}^{2}$ at $(0,0)$.

Mapping between a set and its power set

Let $A,B,X$ be sets such that $A\cup B = X$ and $A \cap B = ∅$. Show that $A = X\backslash B$ and $B = X\backslash A$.

If we have $f : x→ y$ with $S \subset x$ what can we say about $f^{-1}f(S)$ and $S$

Find $\sup\left\{ \frac{m}{|m| + n }\right\} $ where $m \in \Bbb{Z}$ and $n \in \Bbb{N}$

Find Taylor serie and radius of convergence

A theory $T$ with only finitely many complete extensions is finitely axiomatizable iff each complete extension of $T$ is finitely axiomatizable

Obtaining condition for existence of two Chords through a single point with their Mid-points on the $x$-Axis

Let $f:[a,b]\to\Bbb R$ be continuous and take any $\epsilon>0$ . Construct a step function $T$ on $[a.b]$ with..

Proof for uniform convergence of sequence of functions

If there is a sequence of structures which are in $K=\text{Mod}(\Phi),\Phi\subseteq FO(\tau)$ then $\mathfrak{B}\in \mathcal{K}$

Check the uniform convergence of $ \sum\limits_{k=1}^{\infty} \left ( \frac{x \sin x}{1+x} \right )^k$ where $x \in [0,1]$

What English sentences are represented by following expressions?

For angles $A$ and $B$ in a triangle, is $\cos\frac B2-\cos \frac A2=\cos B-\cos A$ enough to conclude that $A=B$?

Limit, supremum and sets

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