Question

$\lim_{x\to+\infty}\frac{\ln(x)}{x^{p}}$

score 83 · Answer 1 · 2020-11-22 10:07:06

83

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$\lim_{x\to+\infty}\frac{\ln(x)}{x^{p}}$

Published on 22 Nov 2020 - 10:07

score 107 · Answer 2 · 2020-11-25 14:31:37

107

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Evaluate $\lim_{x \rightarrow \pi/2}\left(\arctan(x/(\tan(x)-x))/(x-\pi/2)\right)?$

Published on 25 Nov 2020 - 14:31

score 46 · Answer 3 · 2020-11-26 02:33:17

46

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Prove that $\{a_n\}$ converges if $|a_n|\le 2$ and $|a_{n+2}-a_{n+1}|\le \frac{1}{8} |a_{n+1}^2-a_n^2|$

Published on 26 Nov 2020 - 2:33

score 102 · Answer 4 · 2020-11-27 11:38:05

102

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Prove that $\lim_\limits{x\to \frac{\pi}{2}}\frac{\cos(3x)}{1+\cos(2x)}$ doesn't exist without L'hopital rule

Published on 27 Nov 2020 - 11:38

score 54 · Answer 5 · 2020-11-27 13:58:02

54

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How to prove $\lim_{n \to \infty} \frac{n}{1+\sqrt{n}}cos(\frac{\pi n}{n+1})= -\infty$?

Published on 27 Nov 2020 - 13:58

score 42 · Answer 6 · 2020-11-28 09:47:25

42

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Find sequences $a_n$ that converges to 1 and $b_n$ that converges to $\infty$ such that $a_n^{b_n}$ converges to 5

Published on 28 Nov 2020 - 9:47

score 281 · Answer 7 · 2020-11-29 19:29:07

281

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Calculating the limit $ \lim_{x \to 0} \frac{e^{\sin^2(x)} - e^x}{\sin(2x)}$ without L'Hospital's rule

Published on 29 Nov 2020 - 19:29

score 87 · Answer 8 · 2020-11-30 12:52:31

87

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If $\;\lim\limits_{x\rightarrow 10}g(x)=a\;$ and if$\;\lim\limits_{x \rightarrow10}\dfrac{f(x)}{g(x)}=b$, find $\lim\limits_{x\rightarrow10}f(x).$

Published on 30 Nov 2020 - 12:52

score 70 · Answer 9 · 2020-12-01 07:46:14

70

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Evaluation of $\lim_{x\to 0^+}\frac{(1+x)^x - 1}{x^2}$

Published on 01 Dec 2020 - 7:46

score 53 · Answer 10 · 2026-03-29 05:50:10

53

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Fundamental proof of calculus and mean value theorem

Published on 29 Mar 2026 - 5:50

score 28 · Answer 11 · 2020-12-03 23:39:30

28

Views

Integrals and the fundamental theorem of calculus

Published on 03 Dec 2020 - 23:39

score 177 · Answer 12 · 2020-12-04 02:55:29

177

Views

$\displaystyle{\lim \limits_{x \to \frac\pi4}\frac{(\csc^2x-2\tan^2x)}{(\cot x-1)}}$ without L'Hôpitals Rule.

Published on 04 Dec 2020 - 2:55

score 128 · Answer 13 · 2020-12-04 13:37:25

128

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limit of $\cos{x}^{\frac{1}{\sin{x}}}$

Published on 04 Dec 2020 - 13:37

score 61 · Answer 14 · 2020-12-04 16:50:36

Find the integer value of a, b such that $\lim_{x \rightarrow 4} \frac{ax-\sqrt{x}+b}{x-4}=\frac{3}{4}$ without using the L'Hôpital's rule.

score 604 · Answer 15 · 2026-04-07 03:56:16

604

Views

Proving a statement using the definition of a limit

Published on 07 Apr 2026 - 3:56

List Question

$\lim_{x\to+\infty}\frac{\ln(x)}{x^{p}}$

Evaluate $\lim_{x \rightarrow \pi/2}\left(\arctan(x/(\tan(x)-x))/(x-\pi/2)\right)?$

Prove that $\{a_n\}$ converges if $|a_n|\le 2$ and $|a_{n+2}-a_{n+1}|\le \frac{1}{8} |a_{n+1}^2-a_n^2|$

Prove that $\lim_\limits{x\to \frac{\pi}{2}}\frac{\cos(3x)}{1+\cos(2x)}$ doesn't exist without L'hopital rule

How to prove $\lim_{n \to \infty} \frac{n}{1+\sqrt{n}}cos(\frac{\pi n}{n+1})= -\infty$?

Find sequences $a_n$ that converges to 1 and $b_n$ that converges to $\infty$ such that $a_n^{b_n}$ converges to 5

Calculating the limit $ \lim_{x \to 0} \frac{e^{\sin^2(x)} - e^x}{\sin(2x)}$ without L'Hospital's rule

If $\;\lim\limits_{x\rightarrow 10}g(x)=a\;$ and if$\;\lim\limits_{x \rightarrow10}\dfrac{f(x)}{g(x)}=b$, find $\lim\limits_{x\rightarrow10}f(x).$

Evaluation of $\lim_{x\to 0^+}\frac{(1+x)^x - 1}{x^2}$

Fundamental proof of calculus and mean value theorem

Integrals and the fundamental theorem of calculus

$\displaystyle{\lim \limits_{x \to \frac\pi4}\frac{(\csc^2x-2\tan^2x)}{(\cot x-1)}}$ without L'Hôpitals Rule.

limit of $\cos{x}^{\frac{1}{\sin{x}}}$

Find the integer value of a, b such that $\lim_{x \rightarrow 4} \frac{ax-\sqrt{x}+b}{x-4}=\frac{3}{4}$ without using the L'Hôpital's rule.

Proving a statement using the definition of a limit

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