Question

Are any two charts in a manifold compatible?

score 1k · Answer 1 · 2026-03-25 15:59:19

1k

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Are any two charts in a manifold compatible?

Published on 25 Mar 2026 - 15:59

score 2.1k · Answer 2 · 2026-03-25 05:59:16

2.1k

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Matrix function is continuous iff its components are continuous

Published on 25 Mar 2026 - 5:59

score 831 · Answer 3 · 2026-03-25 06:27:56

831

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Prove that $x\mapsto e^x$ is continuous at $x_0 = 1$ ($\delta-\varepsilon$ proof)

Published on 25 Mar 2026 - 6:27

score 50 · Answer 4 · 2018-04-02 19:13:16

50

Views

Find a function continuous on $[0,2]$ differentiable on $(0,1) ,(1,2)$

Published on 02 Apr 2018 - 19:13

score 219 · Answer 5 · 2026-03-30 04:54:52

219

Views

What does "monotone functions are converging to a continuous limit" mean?

Published on 30 Mar 2026 - 4:54

score 30 · Answer 6 · 2018-04-03 11:13:55

30

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How to make the function $f(x)= x^{{(x-2)}^{-1}}$ continuous at $x=2$

Published on 03 Apr 2018 - 11:13

score 162 · Answer 7 · 2018-04-03 14:25:49

Suppose the function $\sqrt{x}$ is continuous at any $c>0$. Show that this function is differentiable at any $c>0$ and find $f'(c)$.

score 120 · Answer 8 · 2026-03-30 12:21:20

120

Views

Prove that this function is NOT differentiable at $c=0$.

Published on 30 Mar 2026 - 12:21

score 345 · Answer 9 · 2026-03-25 00:02:20

345

Views

Functions agreeing on dense sets: weakest separation axiom

Published on 25 Mar 2026 - 0:02

score 47 · Answer 10 · 2018-04-04 01:12:03

47

Views

Show that for values of $y \geq 1$, the equation $y^2$cos $x-e^x = 0$ has a solution for $x$ lying in the interval $[0, \pi/2)$.

Published on 04 Apr 2018 - 1:12

score 661 · Answer 11 · 2026-03-25 06:27:48

661

Views

Proving $f(z)$ is continuous on whole complex plane

Published on 25 Mar 2026 - 6:27

score 255 · Answer 12 · 2018-04-04 03:24:52

255

Views

Proving a continuous function on a closed interval that never repeats a value is strictly increasing

Published on 04 Apr 2018 - 3:24

score 61 · Answer 13 · 2018-04-04 08:25:14

61

Views

Doubt on simplification of function in limits

Published on 04 Apr 2018 - 8:25

score 249 · Answer 14 · 2018-04-04 14:50:42

249

Views

Prove that the function $ f : \Bbb R \to \Bbb R$ is continuous at $ x = 0$ and discontinuous at every $x \ne 0$.

Published on 04 Apr 2018 - 14:50

score 118 · Answer 15 · 2018-04-04 19:27:55

What can I say about the continuity of the function $f(x)=\sin(x)$ if $x$ is rational, and $f(x)=0$ otherwise?

List Question

Are any two charts in a manifold compatible?

Matrix function is continuous iff its components are continuous

Prove that $x\mapsto e^x$ is continuous at $x_0 = 1$ ($\delta-\varepsilon$ proof)

Find a function continuous on $[0,2]$ differentiable on $(0,1) ,(1,2)$

What does "monotone functions are converging to a continuous limit" mean?

How to make the function $f(x)= x^{{(x-2)}^{-1}}$ continuous at $x=2$

Suppose the function $\sqrt{x}$ is continuous at any $c>0$. Show that this function is differentiable at any $c>0$ and find $f'(c)$.

Prove that this function is NOT differentiable at $c=0$.

Functions agreeing on dense sets: weakest separation axiom

Show that for values of $y \geq 1$, the equation $y^2$cos $x-e^x = 0$ has a solution for $x$ lying in the interval $[0, \pi/2)$.

Proving $f(z)$ is continuous on whole complex plane

Proving a continuous function on a closed interval that never repeats a value is strictly increasing

Doubt on simplification of function in limits

Prove that the function $ f : \Bbb R \to \Bbb R$ is continuous at $ x = 0$ and discontinuous at every $x \ne 0$.

What can I say about the continuity of the function $f(x)=\sin(x)$ if $x$ is rational, and $f(x)=0$ otherwise?

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