Question

How fast the solution of $\frac{e^x}{e^x-1}-\frac{1}{x}=\frac{1}{n}$ goes to $-\infty$ as $n\to\infty$?

score 53 · Answer 1 · 2022-10-18 22:02:18

53

Views

How fast the solution of $\frac{e^x}{e^x-1}-\frac{1}{x}=\frac{1}{n}$ goes to $-\infty$ as $n\to\infty$?

Published on 18 Oct 2022 - 22:02

score 75 · Answer 2 · 2022-10-25 18:17:37

75

Views

Can I find a smooth function $f^+$ such that $f \leq f^+$ when $f \geq 0$ is non decreasing?

Published on 25 Oct 2022 - 18:17

score 64 · Answer 3 · 2022-10-27 23:57:44

64

Views

Integral of a continuous function at $x=0$.

Published on 27 Oct 2022 - 23:57

score 54 · Answer 4 · 2022-11-01 17:40:56

54

Views

Prove the inequality $\int_{0}^{(n+(1/2))π} \lvert \sinα \rvert /α > (2/π^2) \log n$

Published on 01 Nov 2022 - 17:40

score 103 · Answer 5 · 2026-03-27 05:36:18

103

Views

Roots of function and its approximation

Published on 27 Mar 2026 - 5:36

score 233 · Answer 6 · 2022-11-09 04:34:24

233

Views

Odd Polynomial approximation of $\frac{1}{x}$ as a polynomial around $0$

Published on 09 Nov 2022 - 4:34

score 39 · Answer 7 · 2022-11-30 21:02:42

39

Views

How to approximate functions of this specified type by polyonomials?

Published on 30 Nov 2022 - 21:02

score 101 · Answer 8 · 2022-12-02 10:43:34

101

Views

Approximation theorem: from inner product space to Hilbert space

Published on 02 Dec 2022 - 10:43

score 45 · Answer 9 · 2022-12-02 16:30:09

45

Views

$\mathscr {L_{2}}$-norm inequality

Published on 02 Dec 2022 - 16:30

score 103 · Answer 10 · 2026-03-29 10:55:37

103

Views

When can a neural network simultaneously approximate a function and its derivative?

Published on 29 Mar 2026 - 10:55

score 19 · Answer 11 · 2026-03-23 15:12:14

19

Views

Show that $T_{1,m} = S_{N}(f)$ when $S_{N}(f)$ is the composite Simpson's rule with N = ${2}^m$ and h = $\frac{b-a}{2^m}$

Published on 23 Mar 2026 - 15:12

score 41 · Answer 12 · 2026-03-25 20:36:02

41

Views

Using upper and lower Riemann sums to show that $Q_{N}(g) \to \int_a^b g(z) dz$

Published on 25 Mar 2026 - 20:36

score 34 · Answer 13 · 2022-12-14 22:41:54

34

Views

Can we characterize the plot of a (not necessarily continuous) function?

Published on 14 Dec 2022 - 22:41

score 170 · Answer 14 · 2022-12-16 13:00:18

170

Views

Polynomial approximations for the arctan on the unit circle

Published on 16 Dec 2022 - 13:00

score 127 · Answer 15 · 2022-12-19 14:35:16

127

Views

If $f$ is bounded away from $0$, are the functions that are close to $f$ in $L^2$ bounded away from zero as well?

Published on 19 Dec 2022 - 14:35

List Question

How fast the solution of $\frac{e^x}{e^x-1}-\frac{1}{x}=\frac{1}{n}$ goes to $-\infty$ as $n\to\infty$?

Can I find a smooth function $f^+$ such that $f \leq f^+$ when $f \geq 0$ is non decreasing?

Integral of a continuous function at $x=0$.

Prove the inequality $\int_{0}^{(n+(1/2))π} \lvert \sinα \rvert /α > (2/π^2) \log n$

Roots of function and its approximation

Odd Polynomial approximation of $\frac{1}{x}$ as a polynomial around $0$

How to approximate functions of this specified type by polyonomials?

Approximation theorem: from inner product space to Hilbert space

$\mathscr {L_{2}}$-norm inequality

When can a neural network simultaneously approximate a function and its derivative?

Show that $T_{1,m} = S_{N}(f)$ when $S_{N}(f)$ is the composite Simpson's rule with N = ${2}^m$ and h = $\frac{b-a}{2^m}$

Using upper and lower Riemann sums to show that $Q_{N}(g) \to \int_a^b g(z) dz$

Can we characterize the plot of a (not necessarily continuous) function?

Polynomial approximations for the arctan on the unit circle

If $f$ is bounded away from $0$, are the functions that are close to $f$ in $L^2$ bounded away from zero as well?

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