Question

Real analysis, uniform convergence : (a) Show that $ f_n: [0, \infty) \to \mathbb R, f_n (x) = x^2e^{-nx} $ converges uniformly on $[0, \infty)$....

score 122 · Answer 1 · 2026-04-16 02:59:57

122

Views

Real analysis, uniform convergence : (a) Show that $ f_n: [0, \infty) \to \mathbb R, f_n (x) = x^2e^{-nx} $ converges uniformly on $[0, \infty)$....

Published on 16 Apr 2026 - 2:59

score 164 · Answer 2 · 2026-04-15 22:53:35

164

Views

Real analysis uniform convergence: Suppose that $f_n : (a,b) \to \mathbb R $ is a sequence of differentiable functions such that there is ...

Published on 15 Apr 2026 - 22:53

score 245 · Answer 3 · 2026-04-12 14:25:54

245

Views

Is $\sum_{n=1}^{\infty} \frac{\sin(n^2x)}{n}$ uniformly convergent on $(0,\pi)$?

Published on 12 Apr 2026 - 14:25

score 879 · Answer 4 · 2026-04-16 04:13:56

879

Views

show that series $\sum_{n=1}^\infty \frac {(-1)^{n-1}}{n+x^2}$ is uniformly convergent for all real values of x

Published on 16 Apr 2026 - 4:13

score 66 · Answer 5 · 2026-04-15 21:24:04

66

Views

Let $f_n, g_n$ : $X \to R$ be two sequences of functions.

Published on 15 Apr 2026 - 21:24

score 114 · Answer 6 · 2026-04-14 07:53:30

114

Views

Uniform convergence of a sequence of continuous functions

Published on 14 Apr 2026 - 7:53

score 133 · Answer 7 · 2026-04-15 09:07:19

133

Views

If $|\frac{c_{n+1}}{c_n}|\leq1+\frac{a}{n}$, where $a<-1$, $a$ does not depend on $n$, then the series $\sum_{n=1}^\infty c_n$ converges absolutely

Published on 15 Apr 2026 - 9:07

score 127 · Answer 8 · 2026-04-17 23:35:48

127

Views

The reciprocal of Abel's Theorem for Limits

Published on 17 Apr 2026 - 23:35

score 45 · Answer 9 · 2026-04-16 16:38:06

45

Views

Uniform convergence of $f_n(x)=3x^2+\dfrac{3x}{n}+\dfrac{1}{n^2}$ for $x\in(0,\infty)$.

Published on 16 Apr 2026 - 16:38

score 70 · Answer 10 · 2026-04-15 17:14:04

70

Views

Uniform convergence of $f_n(x)=n\ln\left (\dfrac{1+nx}{nx}\right)$ at $(0,\infty)$.

Published on 15 Apr 2026 - 17:14

score 49 · Answer 11 · 2026-04-15 00:18:30

49

Views

Meaning of uniform limit to boundary condition

Published on 15 Apr 2026 - 0:18

score 137 · Answer 12 · 2026-04-17 05:54:04

137

Views

Why is $f_n(x) = \int_{0}^{1}f_{n-1}(t)\sin(x-t)dt $ uniformly convergent?

Published on 17 Apr 2026 - 5:54

score 38 · Answer 13 · 2026-04-12 15:34:21

38

Views

Convergence of Operator Values implies Convergence

Published on 12 Apr 2026 - 15:34

score 59 · Answer 14 · 2026-04-16 06:15:25

59

Views

Uniform convergence and second derivative

Published on 16 Apr 2026 - 6:15

score 289 · Answer 15 · 2026-04-14 11:26:12

289

Views

Why does Mittag-Leffler's theorem work over the entire complex plane?

Published on 14 Apr 2026 - 11:26

List Question

Real analysis, uniform convergence : (a) Show that $ f_n: [0, \infty) \to \mathbb R, f_n (x) = x^2e^{-nx} $ converges uniformly on $[0, \infty)$....

Real analysis uniform convergence: Suppose that $f_n : (a,b) \to \mathbb R $ is a sequence of differentiable functions such that there is ...

Is $\sum_{n=1}^{\infty} \frac{\sin(n^2x)}{n}$ uniformly convergent on $(0,\pi)$?

show that series $\sum_{n=1}^\infty \frac {(-1)^{n-1}}{n+x^2}$ is uniformly convergent for all real values of x

Let $f_n, g_n$ : $X \to R$ be two sequences of functions.

Uniform convergence of a sequence of continuous functions

If $|\frac{c_{n+1}}{c_n}|\leq1+\frac{a}{n}$, where $a<-1$, $a$ does not depend on $n$, then the series $\sum_{n=1}^\infty c_n$ converges absolutely

The reciprocal of Abel's Theorem for Limits

Uniform convergence of $f_n(x)=3x^2+\dfrac{3x}{n}+\dfrac{1}{n^2}$ for $x\in(0,\infty)$.

Uniform convergence of $f_n(x)=n\ln\left (\dfrac{1+nx}{nx}\right)$ at $(0,\infty)$.

Meaning of uniform limit to boundary condition

Why is $f_n(x) = \int_{0}^{1}f_{n-1}(t)\sin(x-t)dt $ uniformly convergent?

Convergence of Operator Values implies Convergence

Uniform convergence and second derivative

Why does Mittag-Leffler's theorem work over the entire complex plane?

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