Question

Continuity of the function $f(x)=\lim\limits_{n \to \infty}[\lim\limits_{t\to 0}[\frac{\sin^2 (n!\pi x)}{\sin^2(n! \pi x)+t^2}]] $, $x \in \mathbb R$

score 235 · Answer 1 · 2026-03-29 08:16:03

235

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Continuity of the function $f(x)=\lim\limits_{n \to \infty}[\lim\limits_{t\to 0}[\frac{\sin^2 (n!\pi x)}{\sin^2(n! \pi x)+t^2}]] $, $x \in \mathbb R$

Published on 29 Mar 2026 - 8:16

score 366 · Answer 2 · 2026-03-31 07:07:17

366

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What is the second derivative of $f^{-1}(g(x))$?

Published on 31 Mar 2026 - 7:07

score 67 · Answer 3 · 2026-04-09 01:56:37

67

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Solution of partiell differential equation using the fundamental solution

Published on 09 Apr 2026 - 1:56

score 175 · Answer 4 · 2026-04-08 23:12:20

175

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A question on Group of homeomorphism of $[0,1]$.

Published on 08 Apr 2026 - 23:12

score 85 · Answer 5 · 2026-04-10 04:41:52

85

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Meaning of infinity in $f:\mathbb R^n\rightarrow \mathbb R\cup \{\pm\infty\}$?

Published on 10 Apr 2026 - 4:41

score 491 · Answer 6 · 2026-04-08 22:26:23

491

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Prove that $\lim_{n\to \infty} (a_1a_2\ldots a_n)^{\frac 1n} = L$ given that $\lim_{n\to \infty} (a_n) = L$

Published on 08 Apr 2026 - 22:26

score 106 · Answer 7 · 2026-04-10 06:30:09

106

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$\lim\limits_{} u_n= 0$ and $\lim\limits_{}v_n = 0$ then why $\lim\frac{u_n}{v_n}$ is not defined

Published on 10 Apr 2026 - 6:30

score 213 · Answer 8 · 2026-04-10 03:11:08

213

Views

Best approximation of a function out of a closed subset

Published on 10 Apr 2026 - 3:11

score 202 · Answer 9 · 2026-04-10 04:41:51

202

Views

Rigorous Proof of Cut Property $\Rightarrow$ Completeness of $\mathbb{R}$

Published on 10 Apr 2026 - 4:41

score 286 · Answer 10 · 2026-04-11 02:17:41

286

Views

Reverse Riesz-Thorin inequality

Published on 11 Apr 2026 - 2:17

score 75 · Answer 11 · 2026-04-05 21:38:07

75

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Square sum of $L^2$ orthonormal basis diverges almost everywhere

Published on 05 Apr 2026 - 21:38

score 1k · Answer 12 · 2026-03-25 07:31:54

1k

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Smooth function with $f^{(n)}=0$ is polynomial

Published on 25 Mar 2026 - 7:31

score 303 · Answer 13 · 2026-04-10 20:47:12

303

Views

How do I calculate the sum of this infinite series? $\sum\limits_{n=1}^{\infty}\frac{1}{4n^{2}-1}$

Published on 10 Apr 2026 - 20:47

score 112 · Answer 14 · 2026-04-09 23:21:01

112

Views

If $g \in L^1$ and $f_n \to f$ a.e. where $|f_n| \leq 1$, then $gf_n \to gf$ uniformly on each compact set.

Published on 09 Apr 2026 - 23:21

score 397 · Answer 15 · 2026-04-09 01:53:28

397

Views

Is the Inverse Function Theorem Global?

Published on 09 Apr 2026 - 1:53

List Question

Continuity of the function $f(x)=\lim\limits_{n \to \infty}[\lim\limits_{t\to 0}[\frac{\sin^2 (n!\pi x)}{\sin^2(n! \pi x)+t^2}]] $, $x \in \mathbb R$

What is the second derivative of $f^{-1}(g(x))$?

Solution of partiell differential equation using the fundamental solution

A question on Group of homeomorphism of $[0,1]$.

Meaning of infinity in $f:\mathbb R^n\rightarrow \mathbb R\cup \{\pm\infty\}$?

Prove that $\lim_{n\to \infty} (a_1a_2\ldots a_n)^{\frac 1n} = L$ given that $\lim_{n\to \infty} (a_n) = L$

$\lim\limits_{} u_n= 0$ and $\lim\limits_{}v_n = 0$ then why $\lim\frac{u_n}{v_n}$ is not defined

Best approximation of a function out of a closed subset

Rigorous Proof of Cut Property $\Rightarrow$ Completeness of $\mathbb{R}$

Reverse Riesz-Thorin inequality

Square sum of $L^2$ orthonormal basis diverges almost everywhere

Smooth function with $f^{(n)}=0$ is polynomial

How do I calculate the sum of this infinite series? $\sum\limits_{n=1}^{\infty}\frac{1}{4n^{2}-1}$

If $g \in L^1$ and $f_n \to f$ a.e. where $|f_n| \leq 1$, then $gf_n \to gf$ uniformly on each compact set.

Is the Inverse Function Theorem Global?

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