Question

Continuity of 1/x/x

score 99 · Answer 1 · 2018-07-20 07:40:37

99

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Continuity of 1/x/x

Published on 20 Jul 2018 - 7:40

score 59 · Answer 2 · 2018-07-20 19:01:22

59

Views

Prove that, the map $x\mapsto=[x]\cos^2{\pi x}$ is discontinuous at every integer points.

Published on 20 Jul 2018 - 19:01

score 156 · Answer 3 · 2018-07-21 14:39:54

156

Views

Determine continuity at $(0,0)$ of the function $\frac{e^{xy}-1}{|x|+|y|}$.

Published on 21 Jul 2018 - 14:39

score 3.4k · Answer 4 · 2026-03-27 02:59:45

3.4k

Views

Continuous homomorphisms of Lie groups are smooth

Published on 27 Mar 2026 - 2:59

score 114 · Answer 5 · 2026-02-23 01:20:03

114

Views

Is functional calculus continuous on elements of the algebra.

Published on 23 Feb 2026 - 1:20

score 2.3k · Answer 6 · 2018-07-22 07:51:28

2.3k

Views

Proving that $\lim_{n \to \infty} \int_0^1 f(x) \sin(nx) \, dx = 0$ if $f : \mathbb R \to \mathbb R$ is continuous

Published on 22 Jul 2018 - 7:51

score 1.1k · Answer 7 · 2026-03-25 14:22:03

1.1k

Views

Drunkard's walk's solution: significance of continuity

Published on 25 Mar 2026 - 14:22

score 37 · Answer 8 · 2018-07-23 08:29:56

37

Views

Finding the point of differentiability of a real valued function.

Published on 23 Jul 2018 - 8:29

score 677 · Answer 9 · 2026-03-30 02:06:38

677

Views

Why is $\int_{[0,1]} \frac{dw}{1-wz}$ is holomorphic in unit disc?

Published on 30 Mar 2026 - 2:06

score 531 · Answer 10 · 2018-07-23 13:39:32

531

Views

Tietze extension theorem on real line

Published on 23 Jul 2018 - 13:39

score 409 · Answer 11 · 2018-07-23 23:28:17

Suppose $f: \mathbb{R} \to \mathbb{R}$ is function such that $f^3$ is continuous on $\mathbb{R}$. Prove that $f$ is continuous on $\mathbb{R}$

score 31 · Answer 12 · 2018-07-24 09:42:32

31

Views

if $u(t)$ is a continuous function, defined on a bounded interval, then $u(t)$ $\in L^2$?

Published on 24 Jul 2018 - 9:42

score 67 · Answer 13 · 2026-03-25 09:23:57

67

Views

Understanding proof of monotonic increasing function and continuity

Published on 25 Mar 2026 - 9:23

score 65 · Answer 14 · 2026-03-25 01:18:30

65

Views

Does piecewise continuity of $f'$ implies that the discontinuities of $f$ are jump discontinuities?

Published on 25 Mar 2026 - 1:18

score 321 · Answer 15 · 2018-07-24 16:29:25

321

Views

Proving $f'$ can't have a jump discontinuity point

Published on 24 Jul 2018 - 16:29

List Question

Continuity of 1/x/x

Prove that, the map $x\mapsto=[x]\cos^2{\pi x}$ is discontinuous at every integer points.

Determine continuity at $(0,0)$ of the function $\frac{e^{xy}-1}{|x|+|y|}$.

Continuous homomorphisms of Lie groups are smooth

Is functional calculus continuous on elements of the algebra.

Proving that $\lim_{n \to \infty} \int_0^1 f(x) \sin(nx) \, dx = 0$ if $f : \mathbb R \to \mathbb R$ is continuous

Drunkard's walk's solution: significance of continuity

Finding the point of differentiability of a real valued function.

Why is $\int_{[0,1]} \frac{dw}{1-wz}$ is holomorphic in unit disc?

Tietze extension theorem on real line

Suppose $f: \mathbb{R} \to \mathbb{R}$ is function such that $f^3$ is continuous on $\mathbb{R}$. Prove that $f$ is continuous on $\mathbb{R}$

if $u(t)$ is a continuous function, defined on a bounded interval, then $u(t)$ $\in L^2$?

Understanding proof of monotonic increasing function and continuity

Does piecewise continuity of $f'$ implies that the discontinuities of $f$ are jump discontinuities?

Proving $f'$ can't have a jump discontinuity point

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