Question

Prove that $x^n e^{-x} $ is uniformly continuous on $[0, \infty)$

score 409 · Answer 1 · 2026-03-26 12:52:53

409

Views

Prove that $x^n e^{-x} $ is uniformly continuous on $[0, \infty)$

Published on 26 Mar 2026 - 12:52

score 57 · Answer 2 · 2026-03-29 15:33:05

57

Views

If f is increasing, then show that g is also increasing

Published on 29 Mar 2026 - 15:33

score 64 · Answer 3 · 2018-10-11 06:19:54

64

Views

$m(x) := \inf\{f(t): t \in [a, x)\}$ and $M(x) := \sup\{f(t): t \in [a, x)\}$ . Prove $m$ and $M$ are continuous from left on $(a,b)$

Published on 11 Oct 2018 - 6:19

score 84 · Answer 4 · 2018-10-11 06:44:04

84

Views

Is it possible to calculate $\int_{-1}^{1}\frac{1}{x}dx$ if the domain of $\frac{1}{x}$ is defined as "all reals except number zero"?

Published on 11 Oct 2018 - 6:44

score 659 · Answer 5 · 2026-03-28 10:16:47

659

Views

Must a continuous and periodic functions have a smallest period?

Published on 28 Mar 2026 - 10:16

score 370 · Answer 6 · 2026-04-03 13:41:15

370

Views

Continuity of the differential operator from $(C^1[0,1],d_\infty)$ to $(C[0,1],d_1)$

Published on 03 Apr 2026 - 13:41

score 253 · Answer 7 · 2026-03-26 11:16:48

253

Views

Uniformly continuous Extension functions and limit points.

Published on 26 Mar 2026 - 11:16

score 42 · Answer 8 · 2026-03-29 05:35:07

42

Views

Continuity through the lens of the uniform norm

Published on 29 Mar 2026 - 5:35

score 170 · Answer 9 · 2026-03-27 23:26:55

170

Views

Stone-Weierstrass applications

Published on 27 Mar 2026 - 23:26

score 91 · Answer 10 · 2026-03-26 12:51:31

91

Views

Understanding uniform continuity and extending a function to a continuous function

Published on 26 Mar 2026 - 12:51

score 1k · Answer 11 · 2018-10-12 07:12:56

1k

Views

Quotient Space and Product

Published on 12 Oct 2018 - 7:12

score 1.5k · Answer 12 · 2018-10-12 07:44:42

1.5k

Views

Revisit "Prove that the inverse image of an open set is open"

Published on 12 Oct 2018 - 7:44

score 32 · Answer 13 · 2026-03-25 07:40:25

32

Views

When is a $(\prod_{\alpha \in J} X_\alpha \to X)$-function continuous?

Published on 25 Mar 2026 - 7:40

score 140 · Answer 14 · 2026-03-30 20:43:04

140

Views

What does it mean when the map $u \mapsto \lVert u \rVert$ is continuous with respect to the norm $\lVert u \rVert_1$

Published on 30 Mar 2026 - 20:43

score 15 · Answer 15 · 2026-03-06 17:14:26

15

Views

Continuity for all $x$ in which of these: $[x], [x]+[-x],[x]+\{x\}^2$,etc.

Published on 06 Mar 2026 - 17:14

List Question

Prove that $x^n e^{-x} $ is uniformly continuous on $[0, \infty)$

If f is increasing, then show that g is also increasing

$m(x) := \inf\{f(t): t \in [a, x)\}$ and $M(x) := \sup\{f(t): t \in [a, x)\}$ . Prove $m$ and $M$ are continuous from left on $(a,b)$

Is it possible to calculate $\int_{-1}^{1}\frac{1}{x}dx$ if the domain of $\frac{1}{x}$ is defined as "all reals except number zero"?

Must a continuous and periodic functions have a smallest period?

Continuity of the differential operator from $(C^1[0,1],d_\infty)$ to $(C[0,1],d_1)$

Uniformly continuous Extension functions and limit points.

Continuity through the lens of the uniform norm

Stone-Weierstrass applications

Understanding uniform continuity and extending a function to a continuous function

Quotient Space and Product

Revisit "Prove that the inverse image of an open set is open"

When is a $(\prod_{\alpha \in J} X_\alpha \to X)$-function continuous?

What does it mean when the map $u \mapsto \lVert u \rVert$ is continuous with respect to the norm $\lVert u \rVert_1$

Continuity for all $x$ in which of these: $[x], [x]+[-x],[x]+\{x\}^2$,etc.

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