Question

Finding a limit including an improper integral: $\lim_{n\to\infty}⁡ \int_0^{\sqrt n} \left({1-\frac{x^2}{n}}\right)^n\,dx$

score 73 · Answer 1 · 2026-03-25 06:24:52

73

Views

Finding a limit including an improper integral: $\lim_{n\to\infty}⁡ \int_0^{\sqrt n} \left({1-\frac{x^2}{n}}\right)^n\,dx$

Published on 25 Mar 2026 - 6:24

score 92 · Answer 2 · 2026-03-25 09:27:43

92

Views

Prove through induction that $\sum_{a=1}^{b}a(b-a)=\frac{b(b-1)(b+6)}{6}$

Published on 25 Mar 2026 - 9:27

score 904 · Answer 3 · 2026-03-26 20:44:27

904

Views

Projecting vectors onto line (finding matrix associated with transformation)

Published on 26 Mar 2026 - 20:44

score 72 · Answer 4 · 2026-04-10 17:40:50

72

Views

If $\frac{df(x_1)}{dx_1}>\frac{df(x_2)}{dx_2} \iff x_1<x_2$, what is the sign of $f''$?

Published on 10 Apr 2026 - 17:40

score 70 · Answer 5 · 2026-04-11 23:30:21

70

Views

"Classical inequality" regarding the Bessel potential space $H^{-1}$

Published on 11 Apr 2026 - 23:30

score 104 · Answer 6 · 2018-01-24 20:51:04

104

Views

Find $\lambda$ for min. value of $\int_{0}^{\pi}\sin^2(x-{\lambda}x)$

Published on 24 Jan 2018 - 20:51

score 295 · Answer 7 · 2026-04-09 00:28:40

295

Views

$\int\limits_{-\infty}^\infty \frac{1}{e^{x^{2}}+1}dx$

Published on 09 Apr 2026 - 0:28

score 70 · Answer 8 · 2026-04-12 09:21:37

70

Views

Limit where ${x\to 0}$

Published on 12 Apr 2026 - 9:21

score 74 · Answer 9 · 2026-04-11 01:28:42

74

Views

How to solve $\lim_{x\to \infty}\bigg( 2^{\frac{1}{x}} - 2^{\frac{x-1}{x+1}}\bigg)$??

Published on 11 Apr 2026 - 1:28

score 840 · Answer 10 · 2026-04-08 22:28:24

840

Views

Given points $P(0, 3, 0) \;\;\; Q(-3, 4, 2) \;\;\; R(-2, 9, 1) \;$ find the measure of ∠PQR

Published on 08 Apr 2026 - 22:28

score 123 · Answer 11 · 2026-04-09 02:55:14

123

Views

Limits of power of fractions

Published on 09 Apr 2026 - 2:55

score 370 · Answer 12 · 2026-04-09 00:08:19

370

Views

Find an equation of the curve that is the intersection of the sphere.

Published on 09 Apr 2026 - 0:08

score 754 · Answer 13 · 2026-03-24 20:32:09

754

Views

Find the derivative of $y=(\tan (x))^{\log (x)}$

Published on 24 Mar 2026 - 20:32

score 150 · Answer 14 · 2026-04-12 15:11:44

150

Views

why does the circle at infinity not contribute the integral?

Published on 12 Apr 2026 - 15:11

score 78 · Answer 15 · 2018-01-25 02:19:29

78

Views

Every continuous function $f:ℝ\to ℝ$ can be presented as a sum of a certain power series.

Published on 25 Jan 2018 - 2:19

List Question

Finding a limit including an improper integral: $\lim_{n\to\infty}⁡ \int_0^{\sqrt n} \left({1-\frac{x^2}{n}}\right)^n\,dx$

Prove through induction that $\sum_{a=1}^{b}a(b-a)=\frac{b(b-1)(b+6)}{6}$

Projecting vectors onto line (finding matrix associated with transformation)

If $\frac{df(x_1)}{dx_1}>\frac{df(x_2)}{dx_2} \iff x_1<x_2$, what is the sign of $f''$?

"Classical inequality" regarding the Bessel potential space $H^{-1}$

Find $\lambda$ for min. value of $\int_{0}^{\pi}\sin^2(x-{\lambda}x)$

$\int\limits_{-\infty}^\infty \frac{1}{e^{x^{2}}+1}dx$

Limit where ${x\to 0}$

How to solve $\lim_{x\to \infty}\bigg( 2^{\frac{1}{x}} - 2^{\frac{x-1}{x+1}}\bigg)$??

Given points $P(0, 3, 0) \;\;\; Q(-3, 4, 2) \;\;\; R(-2, 9, 1) \;$ find the measure of ∠PQR

Limits of power of fractions

Find an equation of the curve that is the intersection of the sphere.

Find the derivative of $y=(\tan (x))^{\log (x)}$

why does the circle at infinity not contribute the integral?

Every continuous function $f:ℝ\to ℝ$ can be presented as a sum of a certain power series.

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