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Exercise about derivability and continuity of a function

score 123 · Answer 1 · 2026-04-12 16:01:24

123

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Exercise about derivability and continuity of a function

Published on 12 Apr 2026 - 16:01

score 41 · Answer 2 · 2026-04-16 05:17:31

41

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Smooth $q$-adic decomposition of unity for $q > 1$ large

Published on 16 Apr 2026 - 5:17

score 149 · Answer 3 · 2026-04-11 14:46:49

149

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Find set $A$ whose limit points are the same as its boundary points

Published on 11 Apr 2026 - 14:46

score 246 · Answer 4 · 2026-04-15 17:16:14

246

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Finding a holomorphic function with real part $u=\frac{x(1+x^2+y^2)}{1+2x^2-2y^2+(x^2+y^2)^2}$.

Published on 15 Apr 2026 - 17:16

score 85 · Answer 5 · 2026-04-15 17:18:25

85

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Prove that $x_n\to x\implies \liminf\limits_{n\to\infty}f(x_n)\leq f(x)$

Published on 15 Apr 2026 - 17:18

score 81 · Answer 6 · 2026-04-15 18:06:19

81

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Prove that $\lim\limits_{x\to 1^{-}}f(x)=-1+\ln 4$ where $f(x)=\sum_{n=1}^{\infty}(-1)^{n-1}\frac{x^{n+1}}{n(n+1)}$

Published on 15 Apr 2026 - 18:06

score 89 · Answer 7 · 2026-04-11 09:10:46

89

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How to prove the Parseval's Formula?

Published on 11 Apr 2026 - 9:10

score 98 · Answer 8 · 2026-04-11 00:15:40

98

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Infinite union of sets with almost full measure

Published on 11 Apr 2026 - 0:15

score 947 · Answer 9 · 2026-04-09 06:17:23

947

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Show that $\{f_n\}$ has a uniformly convergent subsequence.

Published on 09 Apr 2026 - 6:17

score 60 · Answer 10 · 2026-04-15 14:35:18

60

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A step in the equality $ \widehat{(T^{}u)}=|\det T|^{-1}((T^{t})^{-1}))^{}\hat{u} $

Published on 15 Apr 2026 - 14:35

score 2.3k · Answer 11 · 2026-04-08 17:52:28

2.3k

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What is Modern Analysis and Abstract Analysis?

Published on 08 Apr 2026 - 17:52

score 169 · Answer 12 · 2026-04-09 07:43:17

169

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Closed-form expression for an integral

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score 22 · Answer 13 · 2026-04-11 07:48:54

22

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Comparing several line functions for finding the minimum values!

Published on 11 Apr 2026 - 7:48

score 136 · Answer 14 · 2026-04-09 17:30:35

136

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Help to construct a function that satisfies the following conditions

Published on 09 Apr 2026 - 17:30

score 249 · Answer 15 · 2026-04-12 11:37:16

249

Views

How to understand the notation $ \frac{\partial f}{\partial \overline{z}} $

Published on 12 Apr 2026 - 11:37

List Question

Exercise about derivability and continuity of a function

Smooth $q$-adic decomposition of unity for $q > 1$ large

Find set $A$ whose limit points are the same as its boundary points

Finding a holomorphic function with real part $u=\frac{x(1+x^2+y^2)}{1+2x^2-2y^2+(x^2+y^2)^2}$.

Prove that $x_n\to x\implies \liminf\limits_{n\to\infty}f(x_n)\leq f(x)$

Prove that $\lim\limits_{x\to 1^{-}}f(x)=-1+\ln 4$ where $f(x)=\sum_{n=1}^{\infty}(-1)^{n-1}\frac{x^{n+1}}{n(n+1)}$

How to prove the Parseval's Formula?

Infinite union of sets with almost full measure

Show that $\{f_n\}$ has a uniformly convergent subsequence.

A step in the equality $ \widehat{(T^{}u)}=|\det T|^{-1}((T^{t})^{-1}))^{}\hat{u} $

What is Modern Analysis and Abstract Analysis?

Closed-form expression for an integral

Comparing several line functions for finding the minimum values!

Help to construct a function that satisfies the following conditions

How to understand the notation $ \frac{\partial f}{\partial \overline{z}} $

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