Question

if a finite limit $L = \lim_{x \rightarrow \infty} f(x) $ exists. Prove that $\exists M >0$ , $|f(x)| \leq M$ for all $x \in [a, +\infty)$

score 200 · Answer 1 · 2018-12-07 05:17:09

200

Views

if a finite limit $L = \lim_{x \rightarrow \infty} f(x) $ exists. Prove that $\exists M >0$ , $|f(x)| \leq M$ for all $x \in [a, +\infty)$

Published on 07 Dec 2018 - 5:17

score 317 · Answer 2 · 2018-12-07 06:10:04

317

Views

test the integral $\int_{0}^{\infty} \frac {x}{3x^4 + 5x^2 +1}dx$ for convergence

Published on 07 Dec 2018 - 6:10

score 261 · Answer 3 · 2018-12-07 08:52:49

261

Views

Conditionally convergent integral

Published on 07 Dec 2018 - 8:52

score 94 · Answer 4 · 2018-12-07 09:57:50

94

Views

Prove that $\int_{0}^{\pi/2} \frac{\sin x}{x} dx$ converges

Published on 07 Dec 2018 - 9:57

score 747 · Answer 5 · 2018-12-08 23:26:18

747

Views

how to show an improper integral is well defined?

Published on 08 Dec 2018 - 23:26

score 442 · Answer 6 · 2026-03-25 00:07:47

442

Views

Evaluate $\int_{-\infty}^\infty \frac{1}{\sqrt{z^2 + 1}}\frac{1}{z - \alpha} dz$.

Published on 25 Mar 2026 - 0:07

score 90 · Answer 7 · 2018-12-10 18:51:15

90

Views

Showing that $\int_{0}^{\infty} u^{-\alpha} \sin(u) \, du >0$ for $0<\alpha<1$

Published on 10 Dec 2018 - 18:51

score 537 · Answer 8 · 2026-03-25 15:42:19

537

Views

solutions to $\int_{-\infty}^\infty \frac{1}{x^n+1}dx$ for even $n$

Published on 25 Mar 2026 - 15:42

score 788 · Answer 9 · 2018-12-12 05:04:53

788

Views

Integral of $\int_0^\infty {x^2}{e^{-3x}}\,dx$

Published on 12 Dec 2018 - 5:04

score 159 · Answer 10 · 2018-12-12 09:08:57

159

Views

For which $p$, $q$ does the improper integral exist?

Published on 12 Dec 2018 - 9:08

score 64 · Answer 11 · 2026-03-27 09:10:41

64

Views

Missing $i$ while evaluating $\int_{-\infty}^{\infty}\frac{e^{iz}}{(z^2+2z+2)^2}$ using residue theorem

Published on 27 Mar 2026 - 9:10

score 123 · Answer 12 · 2026-03-25 23:16:29

123

Views

Need help computing the double integral $\int_{0}^{\infty} \int_{0}^{\infty} \frac{f(x + y)}{x + y} \mathop{dy} \mathop{dx}$

Published on 25 Mar 2026 - 23:16

score 297 · Answer 13 · 2026-03-29 14:02:09

297

Views

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

Published on 29 Mar 2026 - 14:02

score 121 · Answer 14 · 2018-12-13 14:56:58

121

Views

Convergence of $\int_0^\infty \frac{\sin x}{x}dx$

Published on 13 Dec 2018 - 14:56

score 137 · Answer 15 · 2026-03-28 03:27:28

137

Views

Closed from of $\int_0^{\infty} \frac{e^{iax}}{x^{n}+1}dx$?

Published on 28 Mar 2026 - 3:27

List Question

if a finite limit $L = \lim_{x \rightarrow \infty} f(x) $ exists. Prove that $\exists M >0$ , $|f(x)| \leq M$ for all $x \in [a, +\infty)$

test the integral $\int_{0}^{\infty} \frac {x}{3x^4 + 5x^2 +1}dx$ for convergence

Conditionally convergent integral

Prove that $\int_{0}^{\pi/2} \frac{\sin x}{x} dx$ converges

how to show an improper integral is well defined?

Evaluate $\int_{-\infty}^\infty \frac{1}{\sqrt{z^2 + 1}}\frac{1}{z - \alpha} dz$.

Showing that $\int_{0}^{\infty} u^{-\alpha} \sin(u) \, du >0$ for $0<\alpha<1$

solutions to $\int_{-\infty}^\infty \frac{1}{x^n+1}dx$ for even $n$

Integral of $\int_0^\infty {x^2}{e^{-3x}}\,dx$

For which $p$, $q$ does the improper integral exist?

Missing $i$ while evaluating $\int_{-\infty}^{\infty}\frac{e^{iz}}{(z^2+2z+2)^2}$ using residue theorem

Need help computing the double integral $\int_{0}^{\infty} \int_{0}^{\infty} \frac{f(x + y)}{x + y} \mathop{dy} \mathop{dx}$

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

Convergence of $\int_0^\infty \frac{\sin x}{x}dx$

Closed from of $\int_0^{\infty} \frac{e^{iax}}{x^{n}+1}dx$?

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