Question

Find an equivalent to $\frac{(2n)!}{2^{2n} (n!)^{2}}$ when ${n \rightarrow \infty}$

score 72 · Answer 1 · 2020-01-08 11:26:45

72

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Find an equivalent to $\frac{(2n)!}{2^{2n} (n!)^{2}}$ when ${n \rightarrow \infty}$

Published on 08 Jan 2020 - 11:26

score 350 · Answer 2 · 2020-01-08 13:37:57

350

Views

Limit as x approaches some constant value

Published on 08 Jan 2020 - 13:37

score 88 · Answer 3 · 2020-01-09 07:33:49

88

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Discussion on choosing the optimal method in finding:$\lim_{x\to 0}\frac{\sqrt{\cos2x}\cdot e^{2x^2}-1}{\ln{(1+2x)\cdot\ln{(1+2\arcsin{x})}}}$

Published on 09 Jan 2020 - 7:33

score 161 · Answer 4 · 2020-01-10 19:48:47

161

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Solution verification: $\lim_{x\to \infty}\Bigg(\frac{\ln(x^2+3x+4)}{\ln(x^2+2x+3)}\Bigg)^{x\ln x}$

Published on 10 Jan 2020 - 19:48

score 95 · Answer 5 · 2026-03-26 13:02:15

95

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Strange behavior of the function $f(x)=\frac{x^2+\ln(\cos(x))}{x^4}$ when $x\to +\infty (-\infty)$

Published on 26 Mar 2026 - 13:02

score 69 · Answer 6 · 2020-01-14 12:16:02

69

Views

Evaluate $\lim_{x\to 0}\frac{e^{-32x}-1}{4x}$ - Without L'Hospital

Published on 14 Jan 2020 - 12:16

score 209 · Answer 7 · 2020-01-15 03:18:35

209

Views

Spivak's Chapter 5 Exercise 15 part xi

Published on 15 Jan 2020 - 3:18

score 398 · Answer 8 · 2020-01-15 05:15:30

398

Views

Solution verification: $\lim_{x\to 0}\frac{e^{2\sin x}\cosh x-1}{\sqrt[3]{x(\cosh x-\cos x)}}$

Published on 15 Jan 2020 - 5:15

score 78 · Answer 9 · 2020-01-17 09:08:01

78

Views

How to calculate this limit? Is it possible to use L'Hopital's rule?

Published on 17 Jan 2020 - 9:08

score 890 · Answer 10 · 2020-01-17 09:28:08

890

Views

$ \lim_{n \to \infty} \cos^2(\pi \sqrt[\leftroot{-2} \uproot{1} 3]{n^3+n^2+2n}), \space n \in N$

Published on 17 Jan 2020 - 9:28

score 63 · Answer 11 · 2020-01-17 16:10:59

63

Views

$\lim_{x \to 0}|x|^{\frac{1}{x^2}}$?

Published on 17 Jan 2020 - 16:10

score 65 · Answer 12 · 2020-01-17 16:35:11

65

Views

$ \lim_{x \to 0^-}xe^{\frac{1}{x}}$?

Published on 17 Jan 2020 - 16:35

score 69 · Answer 13 · 2020-01-18 17:19:07

69

Views

How to find: $\lim_{x\to 0}\frac{\ln(e+x^2)-\cos x}{e^{x^2}-\cos x}$

Published on 18 Jan 2020 - 17:19

score 161 · Answer 14 · 2020-01-19 14:17:52

161

Views

Solution verification:$\lim_{x\to 2}\frac{\ln(x-1)}{3^{x-2}-5^{-x+2}}$

Published on 19 Jan 2020 - 14:17

score 62 · Answer 15 · 2020-01-19 23:36:55

62

Views

limits of natural log

Published on 19 Jan 2020 - 23:36

List Question

Find an equivalent to $\frac{(2n)!}{2^{2n} (n!)^{2}}$ when ${n \rightarrow \infty}$

Limit as x approaches some constant value

Discussion on choosing the optimal method in finding:$\lim_{x\to 0}\frac{\sqrt{\cos2x}\cdot e^{2x^2}-1}{\ln{(1+2x)\cdot\ln{(1+2\arcsin{x})}}}$

Solution verification: $\lim_{x\to \infty}\Bigg(\frac{\ln(x^2+3x+4)}{\ln(x^2+2x+3)}\Bigg)^{x\ln x}$

Strange behavior of the function $f(x)=\frac{x^2+\ln(\cos(x))}{x^4}$ when $x\to +\infty (-\infty)$

Evaluate $\lim_{x\to 0}\frac{e^{-32x}-1}{4x}$ - Without L'Hospital

Spivak's Chapter 5 Exercise 15 part xi

Solution verification: $\lim_{x\to 0}\frac{e^{2\sin x}\cosh x-1}{\sqrt[3]{x(\cosh x-\cos x)}}$

How to calculate this limit? Is it possible to use L'Hopital's rule?

$ \lim_{n \to \infty} \cos^2(\pi \sqrt[\leftroot{-2} \uproot{1} 3]{n^3+n^2+2n}), \space n \in N$

$\lim_{x \to 0}|x|^{\frac{1}{x^2}}$?

$ \lim_{x \to 0^-}xe^{\frac{1}{x}}$?

How to find: $\lim_{x\to 0}\frac{\ln(e+x^2)-\cos x}{e^{x^2}-\cos x}$

Solution verification:$\lim_{x\to 2}\frac{\ln(x-1)}{3^{x-2}-5^{-x+2}}$

limits of natural log

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