Question

Show that if $f$ is continuous at a point then there exists a a $\delta $-neighborhood where $f$ is uniform continuous.

score 1k · Answer 1 · 2026-04-13 23:45:54

Show that if $f$ is continuous at a point then there exists a a $\delta $-neighborhood where $f$ is uniform continuous.

score 90 · Answer 2 · 2026-04-16 01:08:24

90

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If $f\in L^{1}((0,1))$, does it hold that $\lim\limits_{n\to+\infty}\int_{0}^{\frac{1}{n}}f(x)\mathrm{d}x=0$?

Published on 16 Apr 2026 - 1:08

score 172 · Answer 3 · 2026-04-11 15:12:58

172

Views

How to prove that $e^k > k$?

Published on 11 Apr 2026 - 15:12

score 28 · Answer 4 · 2026-04-11 11:06:48

28

Views

Show that if $f: D\to \mathbb R^m$ is $\mathcal C^1$, then for $x,y \in D$ we have that $f(x)-f(y)=\int_0^1 df(tx+(1-t)y)\cdot (x-y)\ dt.$

Published on 11 Apr 2026 - 11:06

score 56 · Answer 5 · 2026-04-11 11:06:49

56

Views

How does one express the length of curves in terms of the elliptic integral

Published on 11 Apr 2026 - 11:06

score 126 · Answer 6 · 2026-04-20 06:24:21

126

Views

Understanding Uniformly Cauchy

Published on 20 Apr 2026 - 6:24

score 93 · Answer 7 · 2026-04-14 02:07:12

93

Views

How to prove this statement concerning oscillation of a function at a point?

Published on 14 Apr 2026 - 2:07

score 276 · Answer 8 · 2026-04-12 00:48:14

276

Views

Proving triangle inequality holds for a specific metric.

Published on 12 Apr 2026 - 0:48

score 63 · Answer 9 · 2026-04-12 01:47:32

63

Views

Am I using the fundamental theorem of calculus correctly in this proof showing $\partial_x\partial_y f=0$ iff $f(x,y)=g(x)+h(y).$

Published on 12 Apr 2026 - 1:47

score 3.6k · Answer 10 · 2026-04-23 13:47:28

3.6k

Views

Prove that a degree-$6$ polynomial has exactly $2$ real roots

Published on 23 Apr 2026 - 13:47

score 206 · Answer 11 · 2026-04-09 00:00:07

206

Views

Finding the existence of limit of a given function.

Published on 09 Apr 2026 - 0:00

score 66 · Answer 12 · 2026-04-12 09:56:27

66

Views

a variant of the Cantor function

Published on 12 Apr 2026 - 9:56

score 88 · Answer 13 · 2026-04-13 11:30:47

88

Views

Does $\lim a_n$ exist?

Published on 13 Apr 2026 - 11:30

score 84 · Answer 14 · 2026-03-24 22:51:54

84

Views

Let $f$ a function with bounded partial derivatives. Find the greatest value that $f$ can achieve at point $(1, 2)$

Published on 24 Mar 2026 - 22:51

score 26 · Answer 15 · 2026-04-15 13:58:10

26

Views

Proving proposition 4.1 in undergraduate analysis

Published on 15 Apr 2026 - 13:58

List Question

Show that if $f$ is continuous at a point then there exists a a $\delta $-neighborhood where $f$ is uniform continuous.

If $f\in L^{1}((0,1))$, does it hold that $\lim\limits_{n\to+\infty}\int_{0}^{\frac{1}{n}}f(x)\mathrm{d}x=0$?

How to prove that $e^k > k$?

Show that if $f: D\to \mathbb R^m$ is $\mathcal C^1$, then for $x,y \in D$ we have that $f(x)-f(y)=\int_0^1 df(tx+(1-t)y)\cdot (x-y)\ dt.$

How does one express the length of curves in terms of the elliptic integral

Understanding Uniformly Cauchy

How to prove this statement concerning oscillation of a function at a point?

Proving triangle inequality holds for a specific metric.

Am I using the fundamental theorem of calculus correctly in this proof showing $\partial_x\partial_y f=0$ iff $f(x,y)=g(x)+h(y).$

Prove that a degree-$6$ polynomial has exactly $2$ real roots

Finding the existence of limit of a given function.

a variant of the Cantor function

Does $\lim a_n$ exist?

Let $f$ a function with bounded partial derivatives. Find the greatest value that $f$ can achieve at point $(1, 2)$

Proving proposition 4.1 in undergraduate analysis

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