Question

Convergence and limit of recursive sequence

score 189 · Answer 1 · 2026-04-14 06:56:49

189

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Convergence and limit of recursive sequence

Published on 14 Apr 2026 - 6:56

score 372 · Answer 2 · 2026-04-15 10:46:24

372

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How to prove that $\sum_{k=1}^n\frac{1}{\sqrt[n]{k!} }\sim \frac{n}{\ln n}$

Published on 15 Apr 2026 - 10:46

score 349 · Answer 3 · 2026-04-15 06:52:13

349

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Limit Properties In Calculus

Published on 15 Apr 2026 - 6:52

score 63 · Answer 4 · 2026-04-17 01:39:11

63

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Given $f(x)=-2\arctan{\left(e^x\right)}+\ln\left(e^x+2\right)$ solve $f(x)=0$.

Published on 17 Apr 2026 - 1:39

score 137 · Answer 5 · 2026-04-16 06:43:58

137

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Show that $\lim_{n\rightarrow \infty}\int_{a}^{\pi/2}\sqrt{n} \cos^n(x)dx=0$ for any $a\in \left(0,\frac{\pi}{2}\right)$

Published on 16 Apr 2026 - 6:43

score 99 · Answer 6 · 2026-04-17 15:12:51

99

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Find limit $x\rightarrow0$ of $f(x)=x^2\cdot\left({\sin{\frac 1 x}}\right)^2$

Published on 17 Apr 2026 - 15:12

score 92 · Answer 7 · 2026-04-17 11:59:09

92

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Evaluate $\lim _{x \to 0} [2x^{-3}(\sin^{-1}x - \tan^{-1}x )]^{2x^{-2}}$=?

Published on 17 Apr 2026 - 11:59

score 64 · Answer 8 · 2026-04-16 14:54:54

64

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Limit of $f(x)=x^2\left(\sin{\frac 1 x}\right)^2$ for $x\rightarrow\pm\infty$

Published on 16 Apr 2026 - 14:54

score 379 · Answer 9 · 2026-04-16 14:21:19

379

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If $f(x) =\frac{1}{3} ( \frac {5}{f(x+2)}+f(x+1))$ then $\underset{x \to \infty}{\lim}f(x) = ?$

Published on 16 Apr 2026 - 14:21

score 199 · Answer 10 · 2026-05-11 05:30:55

199

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Determine the limit distribution of $\frac{\max\{X_1, X_2,...,X_n \}}{n}$ as $n \to\infty$

Published on 11 May 2026 - 5:30

score 40 · Answer 11 · 2026-04-14 22:09:42

40

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Question on proving $\lim_{x\to a^{+}} f(x)$ exists

Published on 14 Apr 2026 - 22:09

score 733 · Answer 12 · 2026-04-10 11:38:51

733

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What is the difference between $\lim_{h\to0}\frac{0}{h}$ and $\lim_{h\to\infty}\frac{0}{h}$?

Published on 10 Apr 2026 - 11:38

score 419 · Answer 13 · 2026-05-04 17:03:07

419

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Differentiability of $f(x)={x^2\sin{(\dfrac{1}{x})}}$ at $x=0$

Published on 04 May 2026 - 17:03

score 51 · Answer 14 · 2026-04-17 08:07:11

51

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Evaluate limit of $x\left|{\log{\left(x+1\right)}}\right|$ for $x\rightarrow(-1)^+$

Published on 17 Apr 2026 - 8:07

score 59 · Answer 15 · 2026-05-14 15:59:30

59

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Finding the limit of a definite integral

Published on 14 May 2026 - 15:59

List Question

Convergence and limit of recursive sequence

How to prove that $\sum_{k=1}^n\frac{1}{\sqrt[n]{k!} }\sim \frac{n}{\ln n}$

Limit Properties In Calculus

Given $f(x)=-2\arctan{\left(e^x\right)}+\ln\left(e^x+2\right)$ solve $f(x)=0$.

Show that $\lim_{n\rightarrow \infty}\int_{a}^{\pi/2}\sqrt{n} \cos^n(x)dx=0$ for any $a\in \left(0,\frac{\pi}{2}\right)$

Find limit $x\rightarrow0$ of $f(x)=x^2\cdot\left({\sin{\frac 1 x}}\right)^2$

Evaluate $\lim _{x \to 0} [2x^{-3}(\sin^{-1}x - \tan^{-1}x )]^{2x^{-2}}$=?

Limit of $f(x)=x^2\left(\sin{\frac 1 x}\right)^2$ for $x\rightarrow\pm\infty$

If $f(x) =\frac{1}{3} ( \frac {5}{f(x+2)}+f(x+1))$ then $\underset{x \to \infty}{\lim}f(x) = ?$

Determine the limit distribution of $\frac{\max\{X_1, X_2,...,X_n \}}{n}$ as $n \to\infty$

Question on proving $\lim_{x\to a^{+}} f(x)$ exists

What is the difference between $\lim_{h\to0}\frac{0}{h}$ and $\lim_{h\to\infty}\frac{0}{h}$?

Differentiability of $f(x)={x^2\sin{(\dfrac{1}{x})}}$ at $x=0$

Evaluate limit of $x\left|{\log{\left(x+1\right)}}\right|$ for $x\rightarrow(-1)^+$

Finding the limit of a definite integral

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