Question

Find the limit: $\lim_{x \rightarrow \infty} \frac{|x|^{n} - (1 + |x|^2)^{\frac{2}{n}}}{(1 + |x|^2)^{\frac{2}{n}}}.$

score 66 · Answer 1 · 2026-04-23 20:54:55

66

Views

Find the limit: $\lim_{x \rightarrow \infty} \frac{|x|^{n} - (1 + |x|^2)^{\frac{2}{n}}}{(1 + |x|^2)^{\frac{2}{n}}}.$

Published on 23 Apr 2026 - 20:54

score 58 · Answer 2 · 2026-04-16 14:07:54

Show the problem: $\lim_{n \to \infty}\frac {\int_0^n f(x) \,dx}{n}=A \Rightarrow \lim_{x \to \infty}f(x) = A$

score 90 · Answer 3 · 2026-04-17 01:05:04

90

Views

If $\lambda_{n} = \int_{0}^{1} \frac{dt}{(1+t)^n}$ , then value of $\lim_{n \to \infty} \lambda_{n}^{1/n}$?

Published on 17 Apr 2026 - 1:05

score 1.2k · Answer 4 · 2026-04-17 08:14:30

1.2k

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Find $\lim_{x\to 0} \frac{\sinh x -\sin x}{\cosh x - \cos x}$

Published on 17 Apr 2026 - 8:14

score 66 · Answer 5 · 2026-04-16 07:31:43

66

Views

Find $\lim_{x\to\infty} \left(\cos\sqrt{\frac{2a}{x}}\right)^{x}$ where $a>0$

Published on 16 Apr 2026 - 7:31

score 38 · Answer 6 · 2026-04-14 13:14:31

38

Views

How to determine if $\sum \frac{(n-\ln(n))^n}{2^n \cdot n^n}$ converges?

Published on 14 Apr 2026 - 13:14

score 66 · Answer 7 · 2026-04-14 07:13:12

66

Views

Limiting set of scaled natural numbers $\mathbb{N}$

Published on 14 Apr 2026 - 7:13

score 51 · Answer 8 · 2026-04-11 07:20:18

51

Views

Evaluating partial differentiability, sequences in $\mathbb R^{2}$

Published on 11 Apr 2026 - 7:20

score 120 · Answer 9 · 2026-04-11 06:41:29

120

Views

Can Greatest integer function and limit be Interchanged

Published on 11 Apr 2026 - 6:41

score 59 · Answer 10 · 2026-04-17 13:54:15

59

Views

Show $\partial_{v}f=\langle v,\nabla f \rangle$ using mean value theorem

Published on 17 Apr 2026 - 13:54

score 39 · Answer 11 · 2026-04-17 05:41:11

39

Views

For $\lim_{x→1}(2−1/x)=1$, finding δ, such that if $0<|x−1|<δ, then |f(x)−1|<0.1$

Published on 17 Apr 2026 - 5:41

score 84 · Answer 12 · 2026-04-15 22:58:16

84

Views

$\lim_{x\to\ \frac{\pi}{2}^-}\frac{1}{x-\frac{\pi}{2}}+\tan{x} $

Published on 15 Apr 2026 - 22:58

score 88 · Answer 13 · 2026-04-17 20:31:42

88

Views

Simplifying a limit with two variables

Published on 17 Apr 2026 - 20:31

score 76 · Answer 14 · 2026-04-16 03:18:16

76

Views

Evaluating $\lim_{x\to \infty} \cos^{x^{2}}\left(\frac{a}{x}\right)$

Published on 16 Apr 2026 - 3:18

score 37 · Answer 15 · 2026-04-11 11:18:36

37

Views

Testing for Continuity

Published on 11 Apr 2026 - 11:18

List Question

Find the limit: $\lim_{x \rightarrow \infty} \frac{|x|^{n} - (1 + |x|^2)^{\frac{2}{n}}}{(1 + |x|^2)^{\frac{2}{n}}}.$

Show the problem: $\lim_{n \to \infty}\frac {\int_0^n f(x) \,dx}{n}=A \Rightarrow \lim_{x \to \infty}f(x) = A$

If $\lambda_{n} = \int_{0}^{1} \frac{dt}{(1+t)^n}$ , then value of $\lim_{n \to \infty} \lambda_{n}^{1/n}$?

Find $\lim_{x\to 0} \frac{\sinh x -\sin x}{\cosh x - \cos x}$

Find $\lim_{x\to\infty} \left(\cos\sqrt{\frac{2a}{x}}\right)^{x}$ where $a>0$

How to determine if $\sum \frac{(n-\ln(n))^n}{2^n \cdot n^n}$ converges?

Limiting set of scaled natural numbers $\mathbb{N}$

Evaluating partial differentiability, sequences in $\mathbb R^{2}$

Can Greatest integer function and limit be Interchanged

Show $\partial_{v}f=\langle v,\nabla f \rangle$ using mean value theorem

For $\lim_{x→1}(2−1/x)=1$, finding δ, such that if $0<|x−1|<δ, then |f(x)−1|<0.1$

$\lim_{x\to\ \frac{\pi}{2}^-}\frac{1}{x-\frac{\pi}{2}}+\tan{x} $

Simplifying a limit with two variables

Evaluating $\lim_{x\to \infty} \cos^{x^{2}}\left(\frac{a}{x}\right)$

Testing for Continuity

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