Question

Evaluate $\lim_{x\to\infty}\left(\frac{x^2}{2x+1}\right)^{\frac1x}$

score 136 · Answer 1 · 2021-09-10 20:36:20

136

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Evaluate $\lim_{x\to\infty}\left(\frac{x^2}{2x+1}\right)^{\frac1x}$

Published on 10 Sep 2021 - 20:36

score 121 · Answer 2 · 2021-09-11 04:39:49

121

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How to find the limit $\displaystyle\lim_{x\rightarrow\infty}\dfrac{(1+x)^n-3}{x^n}?$

Published on 11 Sep 2021 - 4:39

score 239 · Answer 3 · 2021-09-11 05:28:33

239

Views

How to show that $\displaystyle\lim_{x\rightarrow0}\dfrac{a^{2x}-2}{x^x}=-1$

Published on 11 Sep 2021 - 5:28

score 143 · Answer 4 · 2021-09-11 11:46:01

143

Views

Find $\lim\limits_{x\rightarrow0}\frac{\sin\{x\}}{\{x\}}$

Published on 11 Sep 2021 - 11:46

score 279 · Answer 5 · 2021-09-15 21:17:16

279

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Stuck solving limit without L'Hospital's rule

Published on 15 Sep 2021 - 21:17

score 33 · Answer 6 · 2021-09-17 01:52:11

33

Views

How to evaluate $\lim\limits_{x \rightarrow \infty}x2^{x}$ without using L'Hospital's rule?

Published on 17 Sep 2021 - 1:52

score 105 · Answer 7 · 2021-09-19 09:36:32

105

Views

Why can't we use the limit law to find the limit of a function after fixing the removable discontinuity?

Published on 19 Sep 2021 - 9:36

score 113 · Answer 8 · 2026-02-26 20:06:06

113

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Combining limits in analysis

Published on 26 Feb 2026 - 20:06

score 186 · Answer 9 · 2021-09-19 16:00:03

186

Views

Limit of expression as x approaches 0

Published on 19 Sep 2021 - 16:00

score 234 · Answer 10 · 2021-09-21 18:43:25

234

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If $f(x)=\frac{e^x}{x}$, evaluate $\lim\limits_{n\to\infty}\frac{f^{(n)}(1)}{n!}$.

Published on 21 Sep 2021 - 18:43

score 58 · Answer 11 · 2021-09-23 00:38:51

58

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$f(x)=\begin{cases}x^2\sum\limits_{r=0}^{\left[\frac{1}{|x|}\right]}r&x\neq0\\k/2&x=0\end{cases}$ ...

Published on 23 Sep 2021 - 0:38

score 1.4k · Answer 12 · 2021-09-25 02:19:15

1.4k

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Why do we add a negative sign in front of a square root of a (negative number squared)?

Published on 25 Sep 2021 - 2:19

score 148 · Answer 13 · 2021-09-25 03:23:37

148

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Solve $\lim_{x\to 1}\frac{\sin(x^2-1)}{x-1}$ without L’Hopital.

Published on 25 Sep 2021 - 3:23

score 218 · Answer 14 · 2021-09-25 10:30:34

218

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$f(x)=\lim\limits_{t\rightarrow0}\frac{\sin(\sin(k\pi/e^{1/t})e^{1/t}[x^2-x+\pi])}{\ln (k+[x]^2)}$ where k is an integer and $x\in \mathbb R$?

Published on 25 Sep 2021 - 10:30

score 85 · Answer 15 · 2021-09-29 19:50:12

85

Views

Can this question be solved in any way other than using l'hopital's rule?

Published on 29 Sep 2021 - 19:50

List Question

Evaluate $\lim_{x\to\infty}\left(\frac{x^2}{2x+1}\right)^{\frac1x}$

How to find the limit $\displaystyle\lim_{x\rightarrow\infty}\dfrac{(1+x)^n-3}{x^n}?$

How to show that $\displaystyle\lim_{x\rightarrow0}\dfrac{a^{2x}-2}{x^x}=-1$

Find $\lim\limits_{x\rightarrow0}\frac{\sin\{x\}}{\{x\}}$

Stuck solving limit without L'Hospital's rule

How to evaluate $\lim\limits_{x \rightarrow \infty}x2^{x}$ without using L'Hospital's rule?

Why can't we use the limit law to find the limit of a function after fixing the removable discontinuity?

Combining limits in analysis

Limit of expression as x approaches 0

If $f(x)=\frac{e^x}{x}$, evaluate $\lim\limits_{n\to\infty}\frac{f^{(n)}(1)}{n!}$.

$f(x)=\begin{cases}x^2\sum\limits_{r=0}^{\left[\frac{1}{|x|}\right]}r&x\neq0\\k/2&x=0\end{cases}$ ...

Why do we add a negative sign in front of a square root of a (negative number squared)?

Solve $\lim_{x\to 1}\frac{\sin(x^2-1)}{x-1}$ without L’Hopital.

$f(x)=\lim\limits_{t\rightarrow0}\frac{\sin(\sin(k\pi/e^{1/t})e^{1/t}[x^2-x+\pi])}{\ln (k+[x]^2)}$ where k is an integer and $x\in \mathbb R$?

Can this question be solved in any way other than using l'hopital's rule?

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