Question

Find $\lim_{n\to\infty}\frac{(a-1)^{-n+1}}{a^{-n-1}}$

score 51 · Answer 1 · 2026-04-16 01:16:17

51

Views

Find $\lim_{n\to\infty}\frac{(a-1)^{-n+1}}{a^{-n-1}}$

Published on 16 Apr 2026 - 1:16

score 117 · Answer 2 · 2026-04-16 10:55:51

117

Views

Prove that $\lim_{n\to\infty}\frac{(n+1)(n+2)\cdots(2n-1)2n}{n^n}=\infty$

Published on 16 Apr 2026 - 10:55

score 107 · Answer 3 · 2026-04-16 07:29:45

107

Views

Prove $\lim\limits_{x \to \pm\infty}\dfrac{x^3+1}{x^2+1}=\infty$ by the definition.

Published on 16 Apr 2026 - 7:29

score 46 · Answer 4 · 2026-04-16 11:56:16

46

Views

Find $p$ such that $f(x) = e^{−\frac1{|x|}}$ is differentiable at $0$

Published on 16 Apr 2026 - 11:56

score 76 · Answer 5 · 2026-04-15 05:34:16

76

Views

Prove that $x_n$ has infinity limit

Published on 15 Apr 2026 - 5:34

score 130 · Answer 6 · 2026-04-12 08:30:48

130

Views

Does existence of limit $x\to 0$ of derivative imply function is differentiable at 0?

Published on 12 Apr 2026 - 8:30

score 49 · Answer 7 · 2026-04-17 11:59:11

49

Views

Evaluate $\lim_{x \to 0} \left( \frac{a \cos x}{a+ b\sin x} \right)^{1/x}$, where is the mistake?

Published on 17 Apr 2026 - 11:59

score 127 · Answer 8 · 2026-04-17 08:56:26

127

Views

Compute $\lim \limits_{n \to \infty}\left(\frac {\sqrt[n]a + \sqrt[n]b}2\right)^{n} ~~~ (a, b>0)$

Published on 17 Apr 2026 - 8:56

score 551 · Answer 9 · 2026-04-12 09:48:42

551

Views

Use relation to determine limit of function

Published on 12 Apr 2026 - 9:48

score 266 · Answer 10 · 2026-04-14 06:44:13

266

Views

Proving that $f(x) = \ln x$ is continuous at $a = 3$.

Published on 14 Apr 2026 - 6:44

score 154 · Answer 11 · 2026-04-16 10:31:48

154

Views

How to solve $\lim_{n \to \infty} \frac{n+n^{\frac{1}{2}}+n^{\frac{1}{3}}+...+n^{\frac{1}{n}}}{n}$

Published on 16 Apr 2026 - 10:31

score 699 · Answer 12 · 2026-04-09 12:38:16

699

Views

Understanding the definition of the limit of a sequence

Published on 09 Apr 2026 - 12:38

score 870 · Answer 13 · 2026-05-14 17:50:58

870

Views

Limit of $\frac{y^4\sin(x)}{x^2+y^4}$ when $(x,y) \to (0,0)$

Published on 14 May 2026 - 17:50

score 41 · Answer 14 · 2026-04-10 03:21:08

41

Views

Which function is "larger" when variable aims to infinity?

Published on 10 Apr 2026 - 3:21

score 63 · Answer 15 · 2026-04-13 20:56:53

63

Views

the difference of functions tends to zero

Published on 13 Apr 2026 - 20:56

List Question

Find $\lim_{n\to\infty}\frac{(a-1)^{-n+1}}{a^{-n-1}}$

Prove that $\lim_{n\to\infty}\frac{(n+1)(n+2)\cdots(2n-1)2n}{n^n}=\infty$

Prove $\lim\limits_{x \to \pm\infty}\dfrac{x^3+1}{x^2+1}=\infty$ by the definition.

Find $p$ such that $f(x) = e^{−\frac1{|x|}}$ is differentiable at $0$

Prove that $x_n$ has infinity limit

Does existence of limit $x\to 0$ of derivative imply function is differentiable at 0?

Evaluate $\lim_{x \to 0} \left( \frac{a \cos x}{a+ b\sin x} \right)^{1/x}$, where is the mistake?

Compute $\lim \limits_{n \to \infty}\left(\frac {\sqrt[n]a + \sqrt[n]b}2\right)^{n} ~~~ (a, b>0)$

Use relation to determine limit of function

Proving that $f(x) = \ln x$ is continuous at $a = 3$.

How to solve $\lim_{n \to \infty} \frac{n+n^{\frac{1}{2}}+n^{\frac{1}{3}}+...+n^{\frac{1}{n}}}{n}$

Understanding the definition of the limit of a sequence

Limit of $\frac{y^4\sin(x)}{x^2+y^4}$ when $(x,y) \to (0,0)$

Which function is "larger" when variable aims to infinity?

the difference of functions tends to zero

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