Question

Prove uniform convergence of $f_{n} (x) = \sqrt{\frac{1}{n^2} +x^2}$ to $f(x) = |x|$

score 97 · Answer 1 · 2026-04-16 20:01:55

97

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Prove uniform convergence of $f_{n} (x) = \sqrt{\frac{1}{n^2} +x^2}$ to $f(x) = |x|$

Published on 16 Apr 2026 - 20:01

score 124 · Answer 2 · 2026-04-16 12:56:18

124

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Pointwise convergence of $\frac{n}{xn+1}$

Published on 16 Apr 2026 - 12:56

score 76 · Answer 3 · 2026-04-16 05:05:31

76

Views

Show that $f_n \rightarrow 0$ in $C([0, 1], \mathbb{R})$

Published on 16 Apr 2026 - 5:05

score 620 · Answer 4 · 2026-04-13 12:25:51

620

Views

Limit of a locally uniformly convergent sequence of continuous functions

Published on 13 Apr 2026 - 12:25

score 199 · Answer 5 · 2026-05-15 07:41:42

199

Views

Uniform Law of Large Numbers - questions on supremum, infimum, and weak vs almost sure continuity

Published on 15 May 2026 - 7:41

score 84 · Answer 6 · 2026-04-17 03:54:53

84

Views

Show some theorem concerning of the uniform convergence on compacts of a sequence of polynomials of order $<k$

Published on 17 Apr 2026 - 3:54

score 50 · Answer 7 · 2026-04-14 03:35:37

50

Views

Does this sequence of function converges uniformly?

Published on 14 Apr 2026 - 3:35

score 698 · Answer 8 · 2026-04-17 15:06:32

698

Views

Proving the sequence $f_{n} = \sqrt{x^{2} + 1/n}$ converges uniformly to $f(x) = |x|$ on $(-1, 1)$.

Published on 17 Apr 2026 - 15:06

score 34 · Answer 9 · 2026-04-09 14:44:42

34

Views

Understanding the solution key to a problem which shows that the integral of a sum equals a given value.

Published on 09 Apr 2026 - 14:44

score 123 · Answer 10 · 2026-04-17 12:12:25

123

Views

Describe the interval where $f_n(x) = \sum_{k=1}^n \frac{x^k}{x^k + 1}$ uniformly converges

Published on 17 Apr 2026 - 12:12

score 68 · Answer 11 · 2026-04-11 11:18:10

68

Views

Prove that the function $f_{n}(x) = \frac{1 - |x|^{n}}{1 + |x|^{n}}$ converges pointwise for $x\in \mathbb{R}$.

Published on 11 Apr 2026 - 11:18

score 21 · Answer 12 · 2026-04-16 14:36:28

21

Views

Uniform convergence of a sequence on limited t range

Published on 16 Apr 2026 - 14:36

score 1.6k · Answer 13 · 2026-04-11 11:15:02

1.6k

Views

Continuous function as pointwise limit but not as uniform limit of a sequence of continuous functions on $[0,1]$

Published on 11 Apr 2026 - 11:15

score 299 · Answer 14 · 2026-04-11 21:18:50

299

Views

Uniform convergence of iterated improper integrals on $(0,\infty)$

Published on 11 Apr 2026 - 21:18

score 1.9k · Answer 15 · 2026-04-14 16:54:23

1.9k

Views

Show that $f_n(x)=\frac{x^{2n}}{1+x^{2n}}$ is not uniformly convergent

Published on 14 Apr 2026 - 16:54

List Question

Prove uniform convergence of $f_{n} (x) = \sqrt{\frac{1}{n^2} +x^2}$ to $f(x) = |x|$

Pointwise convergence of $\frac{n}{xn+1}$

Show that $f_n \rightarrow 0$ in $C([0, 1], \mathbb{R})$

Limit of a locally uniformly convergent sequence of continuous functions

Uniform Law of Large Numbers - questions on supremum, infimum, and weak vs almost sure continuity

Show some theorem concerning of the uniform convergence on compacts of a sequence of polynomials of order $<k$

Does this sequence of function converges uniformly?

Proving the sequence $f_{n} = \sqrt{x^{2} + 1/n}$ converges uniformly to $f(x) = |x|$ on $(-1, 1)$.

Understanding the solution key to a problem which shows that the integral of a sum equals a given value.

Describe the interval where $f_n(x) = \sum_{k=1}^n \frac{x^k}{x^k + 1}$ uniformly converges

Prove that the function $f_{n}(x) = \frac{1 - |x|^{n}}{1 + |x|^{n}}$ converges pointwise for $x\in \mathbb{R}$.

Uniform convergence of a sequence on limited t range

Continuous function as pointwise limit but not as uniform limit of a sequence of continuous functions on $[0,1]$

Uniform convergence of iterated improper integrals on $(0,\infty)$

Show that $f_n(x)=\frac{x^{2n}}{1+x^{2n}}$ is not uniformly convergent

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