Question

Find $\lim \limits_{n \to \infty} \int_0^1 f(x) g(x^n) dx$

score 137 · Answer 1 · 2026-04-17 14:44:22

137

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Find $\lim \limits_{n \to \infty} \int_0^1 f(x) g(x^n) dx$

Published on 17 Apr 2026 - 14:44

score 101 · Answer 2 · 2026-04-17 00:16:14

101

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Let $f:[−1, 1] \to \mathbb R$ be defined by $f(x) = \frac{x^2+ [\sin\pi x]}{1+|x|}$

Published on 17 Apr 2026 - 0:16

score 149 · Answer 3 · 2026-04-17 04:47:21

149

Views

For positive $a_1,a_2,a_3......,a_p $ Find $\lim_{n\rightarrow \infty} {\sqrt[n] \frac{a_1^n +a_2^n +........+a_p^n}{p}}$

Published on 17 Apr 2026 - 4:47

score 154 · Answer 4 · 2026-04-15 23:10:55

154

Views

Evaluating $\lim_{n\to\infty}\sum_{k=1}^n \frac{\pi k}{2n}\int_0^1 x^{2n}\sin\frac{\pi x}{2}dx$

Published on 15 Apr 2026 - 23:10

score 1.2k · Answer 5 · 2026-05-14 08:42:55

1.2k

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Show that if $(x_n)\rightarrow 2$ then $(1/x_n)\rightarrow 1/2$

Published on 14 May 2026 - 8:42

score 1.4k · Answer 6 · 2026-04-12 05:00:06

1.4k

Views

Show that $\lim\limits_{n \to \infty}\sin n^2$ does not exist.

Published on 12 Apr 2026 - 5:00

score 102 · Answer 7 · 2026-04-12 00:56:41

102

Views

Why is the inequality changed from $<$ to $\le$ when taking the limit in the case below?

Published on 12 Apr 2026 - 0:56

score 127 · Answer 8 · 2026-04-11 08:44:48

127

Views

Isoceles triangle inscribed inside circle

Published on 11 Apr 2026 - 8:44

score 65 · Answer 9 · 2026-05-11 07:18:22

65

Views

A subsequence of the worst-case subsequence

Published on 11 May 2026 - 7:18

score 425 · Answer 10 · 2026-04-12 00:05:30

425

Views

Limit of a state-transition matrix

Published on 12 Apr 2026 - 0:05

score 94 · Answer 11 · 2026-04-28 09:05:18

94

Views

Is this function continuous at $x = 0$?

Published on 28 Apr 2026 - 9:05

score 428 · Answer 12 · 2026-04-25 03:43:27

428

Views

How can I calculate $\lim_{n \rightarrow \infty} \frac {e^n(2n)!}{(4n)^nn!}$

Published on 25 Apr 2026 - 3:43

score 239 · Answer 13 · 2026-04-29 17:18:41

239

Views

what is the value of the function $\exp(-\frac{1}{x^2})$ at the origin?

Published on 29 Apr 2026 - 17:18

score 74 · Answer 14 · 2026-04-13 14:40:41

74

Views

Exponential Limit

Published on 13 Apr 2026 - 14:40

score 114 · Answer 15 · 2026-04-13 00:56:26

114

Views

How do you evaluate limit of $\frac{\sqrt{a+x} - \sqrt a}{x\sqrt a(\sqrt{a+x})}$ when $x$ tends to $0$?

Published on 13 Apr 2026 - 0:56

List Question

Find $\lim \limits_{n \to \infty} \int_0^1 f(x) g(x^n) dx$

Let $f:[−1, 1] \to \mathbb R$ be defined by $f(x) = \frac{x^2+ [\sin\pi x]}{1+|x|}$

For positive $a_1,a_2,a_3......,a_p $ Find $\lim_{n\rightarrow \infty} {\sqrt[n] \frac{a_1^n +a_2^n +........+a_p^n}{p}}$

Evaluating $\lim_{n\to\infty}\sum_{k=1}^n \frac{\pi k}{2n}\int_0^1 x^{2n}\sin\frac{\pi x}{2}dx$

Show that if $(x_n)\rightarrow 2$ then $(1/x_n)\rightarrow 1/2$

Show that $\lim\limits_{n \to \infty}\sin n^2$ does not exist.

Why is the inequality changed from $<$ to $\le$ when taking the limit in the case below?

Isoceles triangle inscribed inside circle

A subsequence of the worst-case subsequence

Limit of a state-transition matrix

Is this function continuous at $x = 0$?

How can I calculate $\lim_{n \rightarrow \infty} \frac {e^n(2n)!}{(4n)^nn!}$

what is the value of the function $\exp(-\frac{1}{x^2})$ at the origin?

Exponential Limit

How do you evaluate limit of $\frac{\sqrt{a+x} - \sqrt a}{x\sqrt a(\sqrt{a+x})}$ when $x$ tends to $0$?

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