Question

Looking for an approximation of $\mathbf{1}_{[0,t]}$ satisfying certain conditions.

score 24 · Answer 1 · 2022-06-22 11:48:02

24

Views

Looking for an approximation of $\mathbf{1}_{[0,t]}$ satisfying certain conditions.

Published on 22 Jun 2022 - 11:48

score 216 · Answer 2 · 2022-06-23 08:51:53

216

Views

Determinining uniform convergence for $f_{n}(x)=\sum_{k=1}^{n}\frac{k}{k^2x^2+2n^2}$ over $\mathbb{R}$

Published on 23 Jun 2022 - 8:51

score 62 · Answer 3 · 2022-06-26 02:56:20

62

Views

Use of limits of sequences for the non-existence

Published on 26 Jun 2022 - 2:56

score 34 · Answer 4 · 2022-06-26 13:38:40

34

Views

Showing a set is open in a topology defined by invariant metric

Published on 26 Jun 2022 - 13:38

score 74 · Answer 5 · 2022-06-27 07:59:08

74

Views

Convergence of the sequence of functions.

Published on 27 Jun 2022 - 7:59

score 36 · Answer 6 · 2022-07-07 10:54:13

36

Views

$\int_{-1}^{f(x+1/n)}g(t)dt$ converges uniformly

Published on 07 Jul 2022 - 10:54

score 60 · Answer 7 · 2022-07-07 22:04:52

60

Views

$f_n\rightrightarrows f$ on $[a+\delta,b-\delta]$. Show $\lim_{n\to\infty} \int_a^b |f_n-f|=0$

Published on 07 Jul 2022 - 22:04

score 31 · Answer 8 · 2022-07-12 22:03:39

31

Views

Show a sequence generating a nonincreasing sequence of function values is bounded if sublevel sets are bounded

Published on 12 Jul 2022 - 22:03

score 45 · Answer 9 · 2022-07-19 08:17:51

45

Views

Condition when the sum of small lengths of limiting curve is equal to limit of sum of small lengths of curve

Published on 19 Jul 2022 - 8:17

score 715 · Answer 10 · 2022-07-25 18:33:08

715

Views

$f$ uniformly continuous, $f_n(x) = f(x + 1/n)$. Show $f_n$ uniformly converges to $f$. Why is uniform continuity needed?

Published on 25 Jul 2022 - 18:33

score 164 · Answer 11 · 2022-07-29 00:00:13

164

Views

Pointwise convergence of polynomials of degree $k$

Published on 29 Jul 2022 - 0:00

score 89 · Answer 12 · 2022-07-29 20:01:21

89

Views

Generating Sequence of Right angled triangle

Published on 29 Jul 2022 - 20:01

score 418 · Answer 13 · 2022-08-02 22:28:28

418

Views

limit $\lim_{k \to \infty} \int_{0}^{1} \frac{kx^k}{1+x} dx$

Published on 02 Aug 2022 - 22:28

score 45 · Answer 14 · 2022-08-04 10:37:25

45

Views

Finding the limit of a linear combination of sequences of functions

Published on 04 Aug 2022 - 10:37

score 40 · Answer 15 · 2022-08-10 20:08:26

40

Views

Show that it's impossible find a pointwise convergence sequence

Published on 10 Aug 2022 - 20:08

List Question

Looking for an approximation of $\mathbf{1}_{[0,t]}$ satisfying certain conditions.

Determinining uniform convergence for $f_{n}(x)=\sum_{k=1}^{n}\frac{k}{k^2x^2+2n^2}$ over $\mathbb{R}$

Use of limits of sequences for the non-existence

Showing a set is open in a topology defined by invariant metric

Convergence of the sequence of functions.

$\int_{-1}^{f(x+1/n)}g(t)dt$ converges uniformly

$f_n\rightrightarrows f$ on $[a+\delta,b-\delta]$. Show $\lim_{n\to\infty} \int_a^b |f_n-f|=0$

Show a sequence generating a nonincreasing sequence of function values is bounded if sublevel sets are bounded

Condition when the sum of small lengths of limiting curve is equal to limit of sum of small lengths of curve

$f$ uniformly continuous, $f_n(x) = f(x + 1/n)$. Show $f_n$ uniformly converges to $f$. Why is uniform continuity needed?

Pointwise convergence of polynomials of degree $k$

Generating Sequence of Right angled triangle

limit $\lim_{k \to \infty} \int_{0}^{1} \frac{kx^k}{1+x} dx$

Finding the limit of a linear combination of sequences of functions

Show that it's impossible find a pointwise convergence sequence

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