Question

Evaluate $\lim_{x \to 0} \frac{\ln\left[\frac{(1-3x)(1+x)^3}{(1+3x)(1-x)^3}\right]}{x^3}$ without L'Hôpital/Taylor/differentiation/integration

score 129 · Answer 1 · 2022-01-08 16:42:46

129

Views

Evaluate $\lim_{x \to 0} \frac{\ln\left[\frac{(1-3x)(1+x)^3}{(1+3x)(1-x)^3}\right]}{x^3}$ without L'Hôpital/Taylor/differentiation/integration

Published on 08 Jan 2022 - 16:42

score 43 · Answer 2 · 2022-01-08 17:14:13

43

Views

how can I use taylor series to approximate these two functions?

Published on 08 Jan 2022 - 17:14

score 171 · Answer 3 · 2022-01-09 05:27:42

171

Views

How to find $\lim_{n\to \infty} \frac{\log(n)}{n}$ without L'Hospital's rule?

Published on 09 Jan 2022 - 5:27

score 60 · Answer 4 · 2022-01-10 16:04:11

60

Views

How can I approximate these two functions?

Published on 10 Jan 2022 - 16:04

score 83 · Answer 5 · 2022-01-10 18:28:48

83

Views

How to solve $\lim_{x\to\infty} \left(\frac{4+x}{1+x}\right)^{4+2x}$ (without l'Hospital maybe?)

Published on 10 Jan 2022 - 18:28

score 87 · Answer 6 · 2022-01-11 18:02:48

87

Views

Solve $\lim_{x\to 0} \frac{\sqrt[2]{\cos(x)}+\sqrt[3]{\cos(x)}+\ldots+\sqrt[n+1]{\cos(x)}-n}{(e^x -1)^2}$

Published on 11 Jan 2022 - 18:02

score 133 · Answer 7 · 2022-01-12 17:11:34

133

Views

how to solve this limit without l'hopital

Published on 12 Jan 2022 - 17:11

score 139 · Answer 8 · 2022-01-15 16:29:14

139

Views

If $f(x)=\frac{1}{3} \biggl ( f(x+1)+\frac{5}{f(x+2)}\biggl)$ and $f(x)>0$, $\forall$ $x\in \mathbb R$ then $\lim_{x \rightarrow \infty} f(x)$ is?

Published on 15 Jan 2022 - 16:29

score 610 · Answer 9 · 2026-04-09 07:19:59

610

Views

How to calculate a limit without using L'Hôpital's Rule

Published on 09 Apr 2026 - 7:19

score 148 · Answer 10 · 2022-01-16 19:33:18

148

Views

Calculating $\lim\limits_{x\to 0} \frac{e^{2x}-1}{3x}$ without using L'Hôpital's rule

Published on 16 Jan 2022 - 19:33

score 104 · Answer 11 · 2022-01-17 07:49:35

104

Views

Evaluate $\lim_{n \rightarrow \infty} \frac{( n^5+2)^{1/4}-(n^2+1)^{1/3}}{(n^4+2)^{1/5}-(n^3+1)^{1/2}}$

Published on 17 Jan 2022 - 7:49

score 123 · Answer 12 · 2022-01-17 15:25:14

123

Views

Is there a closed form for $\lim_{N\to\infty}\left(2\sqrt{N+1}\;-\;\sum_{n=1}^N\frac1{\sqrt{n}}\right)\;$?

Published on 17 Jan 2022 - 15:25

score 73 · Answer 13 · 2022-01-20 03:51:43

73

Views

Without l'Hôpital or series, $\lim_{y\to 0}\big(\sin(\tan y) - \tan y\big)/(my^n)$ $=1\,$?

Published on 20 Jan 2022 - 3:51

score 68 · Answer 14 · 2022-01-23 16:26:43

68

Views

Calculate the limit using stolz theorem

Published on 23 Jan 2022 - 16:26

score 44 · Answer 15 · 2026-04-08 18:46:38

44

Views

Limit calculation using Taylor

Published on 08 Apr 2026 - 18:46

List Question

Evaluate $\lim_{x \to 0} \frac{\ln\left[\frac{(1-3x)(1+x)^3}{(1+3x)(1-x)^3}\right]}{x^3}$ without L'Hôpital/Taylor/differentiation/integration

how can I use taylor series to approximate these two functions?

How to find $\lim_{n\to \infty} \frac{\log(n)}{n}$ without L'Hospital's rule?

How can I approximate these two functions?

How to solve $\lim_{x\to\infty} \left(\frac{4+x}{1+x}\right)^{4+2x}$ (without l'Hospital maybe?)

Solve $\lim_{x\to 0} \frac{\sqrt[2]{\cos(x)}+\sqrt[3]{\cos(x)}+\ldots+\sqrt[n+1]{\cos(x)}-n}{(e^x -1)^2}$

how to solve this limit without l'hopital

If $f(x)=\frac{1}{3} \biggl ( f(x+1)+\frac{5}{f(x+2)}\biggl)$ and $f(x)>0$, $\forall$ $x\in \mathbb R$ then $\lim_{x \rightarrow \infty} f(x)$ is?

How to calculate a limit without using L'Hôpital's Rule

Calculating $\lim\limits_{x\to 0} \frac{e^{2x}-1}{3x}$ without using L'Hôpital's rule

Evaluate $\lim_{n \rightarrow \infty} \frac{( n^5+2)^{1/4}-(n^2+1)^{1/3}}{(n^4+2)^{1/5}-(n^3+1)^{1/2}}$

Is there a closed form for $\lim_{N\to\infty}\left(2\sqrt{N+1}\;-\;\sum_{n=1}^N\frac1{\sqrt{n}}\right)\;$?

Without l'Hôpital or series, $\lim_{y\to 0}\big(\sin(\tan y) - \tan y\big)/(my^n)$ $=1\,$?

Calculate the limit using stolz theorem

Limit calculation using Taylor

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