Question

let $f(x) = e^{-x^2} \cos(e^{x^2})$ Prove/Disprove $\forall k \in N, \lim_{|x| \to \infty} |x^k f'(x)|=0$

score 34 · Answer 1 · 2026-04-17 08:48:49

34

Views

let $f(x) = e^{-x^2} \cos(e^{x^2})$ Prove/Disprove $\forall k \in N, \lim_{|x| \to \infty} |x^k f'(x)|=0$

Published on 17 Apr 2026 - 8:48

score 133 · Answer 2 · 2026-04-23 06:41:54

133

Views

Solving the two ODEs $\frac {dv}{dt}+\frac va=F$ and $c-\frac 12 \frac {du}{dt}-\frac ua=0$

Published on 23 Apr 2026 - 6:41

score 84 · Answer 3 · 2026-04-26 06:16:40

84

Views

Study the convergence of $\sum_\limits{n=1}^{\infty}\frac{(-1)^n}{(x+n)^p}$

Published on 26 Apr 2026 - 6:16

score 1.5k · Answer 4 · 2026-05-04 12:22:40

1.5k

Views

Fubini's Theorem contradiction

Published on 04 May 2026 - 12:22

score 4.5k · Answer 5 · 2026-05-10 14:05:02

4.5k

Views

Starting index for geometric series test

Published on 10 May 2026 - 14:05

score 48 · Answer 6 · 2026-05-10 20:08:24

48

Views

Minimum of $F(\alpha x + \beta) + F(-\alpha x + \beta)$where $F$ is the cdf of a standard normal

Published on 10 May 2026 - 20:08

score 548 · Answer 7 · 2026-05-04 12:24:55

548

Views

Explaining $\int_{-1}^1\frac{1}{1+x^2}\,dx = \frac{\pi}{2}$.

Published on 04 May 2026 - 12:24

score 87 · Answer 8 · 2026-04-23 02:23:51

87

Views

Maximum and minimum points

Published on 23 Apr 2026 - 2:23

score 26 · Answer 9 · 2026-04-25 02:21:57

26

Views

what's a representative mapping of a rotation around the $z-$axis?

Published on 25 Apr 2026 - 2:21

score 75 · Answer 10 · 2026-04-24 15:49:08

75

Views

Construct a path and calculate the integrals

Published on 24 Apr 2026 - 15:49

score 68 · Answer 11 · 2026-04-14 02:31:55

68

Views

Using the $5$-th order Maclaurin polynomial of $f(x) = e^x$ to approximate $f(-1)$

Published on 14 Apr 2026 - 2:31

score 50 · Answer 12 · 2026-04-16 04:53:46

50

Views

Convergence of $x_n(t)=\frac{2nt}{1+n^2t^2}$ in $C_{[0,1]}$ and $C_{[1,\infty]}$

Published on 16 Apr 2026 - 4:53

score 112 · Answer 13 · 2026-04-14 14:21:40

112

Views

A question on Lagrange's Mean Value theorem.

Published on 14 Apr 2026 - 14:21

score 80 · Answer 14 · 2026-04-15 23:35:54

80

Views

Finding all positive $a$ such that $a^x \geq x$ for all real $x$

Published on 15 Apr 2026 - 23:35

score 59 · Answer 15 · 2026-05-10 20:14:07

59

Views

Small trouble in finding Laplace Transform of $\sqrt{t}$ without using Gamma function

Published on 10 May 2026 - 20:14

List Question

let $f(x) = e^{-x^2} \cos(e^{x^2})$ Prove/Disprove $\forall k \in N, \lim_{|x| \to \infty} |x^k f'(x)|=0$

Solving the two ODEs $\frac {dv}{dt}+\frac va=F$ and $c-\frac 12 \frac {du}{dt}-\frac ua=0$

Study the convergence of $\sum_\limits{n=1}^{\infty}\frac{(-1)^n}{(x+n)^p}$

Fubini's Theorem contradiction

Starting index for geometric series test

Minimum of $F(\alpha x + \beta) + F(-\alpha x + \beta)$where $F$ is the cdf of a standard normal

Explaining $\int_{-1}^1\frac{1}{1+x^2}\,dx = \frac{\pi}{2}$.

Maximum and minimum points

what's a representative mapping of a rotation around the $z-$axis?

Construct a path and calculate the integrals

Using the $5$-th order Maclaurin polynomial of $f(x) = e^x$ to approximate $f(-1)$

Convergence of $x_n(t)=\frac{2nt}{1+n^2t^2}$ in $C_{[0,1]}$ and $C_{[1,\infty]}$

A question on Lagrange's Mean Value theorem.

Finding all positive $a$ such that $a^x \geq x$ for all real $x$

Small trouble in finding Laplace Transform of $\sqrt{t}$ without using Gamma function

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