Question

$a, b$ so $f(x)=x^2\sin(1/x+1), x>0$ $f(x)= ax+b, x \le 0$ becomes continuous at $x=0$

score 35 · Answer 1 · 2026-03-30 07:42:42

35

Views

$a, b$ so $f(x)=x^2\sin(1/x+1), x>0$ $f(x)= ax+b, x \le 0$ becomes continuous at $x=0$

Published on 30 Mar 2026 - 7:42

score 85 · Answer 2 · 2026-03-30 07:43:58

85

Views

Showing that $f(x)$ is well-defined and continuous on $\mathbb{R} \setminus \mathbb{Z}$.

Published on 30 Mar 2026 - 7:43

score 32 · Answer 3 · 2026-04-07 16:18:40

32

Views

Unique solution of a equation

Published on 07 Apr 2026 - 16:18

score 56 · Answer 4 · 2026-03-27 03:42:31

56

Views

show that function $f:\mathbb{R \to\mathbb{R}}$ defined by $f(x)=|x|^{p}$ for $p\geq1$ is a convex function.

Published on 27 Mar 2026 - 3:42

score 262 · Answer 5 · 2026-03-28 08:29:57

262

Views

About the proof: $\mathbb Q$ is not locally compact

Published on 28 Mar 2026 - 8:29

score 36 · Answer 6 · 2026-04-07 06:17:16

36

Views

Concavity function

Published on 07 Apr 2026 - 6:17

score 68 · Answer 7 · 2026-03-26 22:16:23

68

Views

How to find $\arg\lim_{n \to \infty}(1+\frac{z}{n})^n$?

Published on 26 Mar 2026 - 22:16

score 174 · Answer 8 · 2026-03-30 01:47:04

174

Views

How does the 1-Lipschitz and uniform boundedness matter in establishing this as a metric?

Published on 30 Mar 2026 - 1:47

score 247 · Answer 9 · 2026-03-30 11:03:29

247

Views

How can I prove that $f(x)=\sum_{k=1}^{\infty}\frac{\{kx\}}{k^{2}}$ is continuous?

Published on 30 Mar 2026 - 11:03

score 77 · Answer 10 · 2026-03-24 23:45:11

77

Views

Is $\frac{1}{x}$ continuosly differentiable on the set $E = (- \infty, 0) \cup (0, \infty)$?

Published on 24 Mar 2026 - 23:45

score 432 · Answer 11 · 2026-03-27 18:27:52

432

Views

Prove that there exists an irrational number $\\a$ such that $x< au< y$ if $x< y$ and $u> 0$.

Published on 27 Mar 2026 - 18:27

score 69 · Answer 12 · 2018-02-28 13:40:01

69

Views

Let $f:\mathbb{C}\rightarrow \mathbb{C}$ be the map given by $f(z)=\sin z-z$. Then image of $f$ is $\mathbb{C}$. (T/F)

Published on 28 Feb 2018 - 13:40

score 187 · Answer 13 · 2026-03-25 13:34:24

187

Views

If $E_1 \cup E_2$ is a disjoint union of subsets of $\mathbb{R}^d$, then $m^(E_1 \cup E_2) = m^(E_1) +m^*(E_2)$ may not hold

Published on 25 Mar 2026 - 13:34

score 46 · Answer 14 · 2026-03-25 14:00:32

46

Views

Doubt on a certain asymptotic formula

Published on 25 Mar 2026 - 14:00

score 36 · Answer 15 · 2026-03-30 10:54:35

36

Views

"Constant" points of an increasing function

Published on 30 Mar 2026 - 10:54

List Question

$a, b$ so $f(x)=x^2\sin(1/x+1), x>0$ $f(x)= ax+b, x \le 0$ becomes continuous at $x=0$

Showing that $f(x)$ is well-defined and continuous on $\mathbb{R} \setminus \mathbb{Z}$.

Unique solution of a equation

show that function $f:\mathbb{R \to\mathbb{R}}$ defined by $f(x)=|x|^{p}$ for $p\geq1$ is a convex function.

About the proof: $\mathbb Q$ is not locally compact

Concavity function

How to find $\arg\lim_{n \to \infty}(1+\frac{z}{n})^n$?

How does the 1-Lipschitz and uniform boundedness matter in establishing this as a metric?

How can I prove that $f(x)=\sum_{k=1}^{\infty}\frac{\{kx\}}{k^{2}}$ is continuous?

Is $\frac{1}{x}$ continuosly differentiable on the set $E = (- \infty, 0) \cup (0, \infty)$?

Prove that there exists an irrational number $\\a$ such that $x< au< y$ if $x< y$ and $u> 0$.

Let $f:\mathbb{C}\rightarrow \mathbb{C}$ be the map given by $f(z)=\sin z-z$. Then image of $f$ is $\mathbb{C}$. (T/F)

If $E_1 \cup E_2$ is a disjoint union of subsets of $\mathbb{R}^d$, then $m^(E_1 \cup E_2) = m^(E_1) +m^*(E_2)$ may not hold

Doubt on a certain asymptotic formula

"Constant" points of an increasing function

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