Question

Find $\lim_{x\to \infty}\left({x \over x^2+1}+{x \over x^2+2}+\cdots +{x\over x^2+x}\right)$

score 169 · Answer 1 · 2026-04-17 04:41:42

169

Views

Find $\lim_{x\to \infty}\left({x \over x^2+1}+{x \over x^2+2}+\cdots +{x\over x^2+x}\right)$

Published on 17 Apr 2026 - 4:41

score 119 · Answer 2 · 2026-04-12 06:38:18

119

Views

How to prove that the function $f$ is continuous on $\mathbb{R}$

Published on 12 Apr 2026 - 6:38

score 139 · Answer 3 · 2026-05-10 22:10:14

139

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Evaluate $\lim_{x\rightarrow\frac{\pi}{2}^\pm}{\log{\left({\frac{1}{\cos^4x}}\right)}-\tan^2{x}}$

Published on 10 May 2026 - 22:10

score 251 · Answer 4 · 2026-04-15 06:50:04

251

Views

Determine the limit and give and $\epsilon-N$ proof of $\lim_{n\rightarrow\infty}\frac{3+(-4)^n}{n^2}$.

Published on 15 Apr 2026 - 6:50

score 84 · Answer 5 · 2026-04-08 18:46:53

84

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Limit verification

Published on 08 Apr 2026 - 18:46

score 1k · Answer 6 · 2026-05-06 02:17:21

1k

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For $f(x,y) = \frac{xy-1}{x^2 y^2-1}$, what is the limit as $(x,y)$ goes to $(1,1)$?

Published on 06 May 2026 - 2:17

score 779 · Answer 7 · 2026-04-16 10:30:27

779

Views

Evaluating $\lim_{n \to \infty}\tan(n\pi/(2n+1))^{1/n}$

Published on 16 Apr 2026 - 10:30

score 114 · Answer 8 · 2026-05-05 03:28:45

114

Views

Suppose $f: \mathbb{R} \to \mathbb{R}$ is twice differentiable. Show that $\lim_{x \to \infty} f'' (x) = 0$, given conditions.

Published on 05 May 2026 - 3:28

score 1.2k · Answer 9 · 2026-04-24 01:09:36

1.2k

Views

Show $f(z) = |z|^2$ is differentiable only at $z = 0$

Published on 24 Apr 2026 - 1:09

score 149 · Answer 10 · 2026-05-05 03:28:50

149

Views

If $f$ is differentiable for $x\neq x_0$ and $\lim_{x\to x_0} f'(x) = c$ then $f'(x_0) = c$

Published on 05 May 2026 - 3:28

score 1.3k · Answer 11 · 2026-04-17 03:37:43

1.3k

Views

Compute $\lim\limits_{n \to \infty} {\frac{1 \cdot 3 \cdot 5 \cdots(2n - 1)}{2 \cdot 4 \cdot 6 \cdots (2n)}}$

Published on 17 Apr 2026 - 3:37

score 187 · Answer 12 · 2026-04-14 05:42:38

187

Views

Limit of sequence exists but might be infinity

Published on 14 Apr 2026 - 5:42

score 62 · Answer 13 · 2026-04-16 14:36:37

62

Views

Prove that the function $f:\mathbb{R}\to\mathbb{R}$ by $f(x)=x^\frac{1}{n}$ is continuous

Published on 16 Apr 2026 - 14:36

score 116 · Answer 14 · 2026-04-14 00:09:40

116

Views

Does this matrix sequence always converge?

Published on 14 Apr 2026 - 0:09

score 140 · Answer 15 · 2026-04-17 18:03:09

140

Views

Evaluate $\lim_{n\to{\infty}}\frac{e(1-\frac{1}{n})^n-1}{n^{\alpha}}=c$

Published on 17 Apr 2026 - 18:03

List Question

Find $\lim_{x\to \infty}\left({x \over x^2+1}+{x \over x^2+2}+\cdots +{x\over x^2+x}\right)$

How to prove that the function $f$ is continuous on $\mathbb{R}$

Evaluate $\lim_{x\rightarrow\frac{\pi}{2}^\pm}{\log{\left({\frac{1}{\cos^4x}}\right)}-\tan^2{x}}$

Determine the limit and give and $\epsilon-N$ proof of $\lim_{n\rightarrow\infty}\frac{3+(-4)^n}{n^2}$.

Limit verification

For $f(x,y) = \frac{xy-1}{x^2 y^2-1}$, what is the limit as $(x,y)$ goes to $(1,1)$?

Evaluating $\lim_{n \to \infty}\tan(n\pi/(2n+1))^{1/n}$

Suppose $f: \mathbb{R} \to \mathbb{R}$ is twice differentiable. Show that $\lim_{x \to \infty} f'' (x) = 0$, given conditions.

Show $f(z) = |z|^2$ is differentiable only at $z = 0$

If $f$ is differentiable for $x\neq x_0$ and $\lim_{x\to x_0} f'(x) = c$ then $f'(x_0) = c$

Compute $\lim\limits_{n \to \infty} {\frac{1 \cdot 3 \cdot 5 \cdots(2n - 1)}{2 \cdot 4 \cdot 6 \cdots (2n)}}$

Limit of sequence exists but might be infinity

Prove that the function $f:\mathbb{R}\to\mathbb{R}$ by $f(x)=x^\frac{1}{n}$ is continuous

Does this matrix sequence always converge?

Evaluate $\lim_{n\to{\infty}}\frac{e(1-\frac{1}{n})^n-1}{n^{\alpha}}=c$

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