limit

**dhiab** · December 7th 2009, 02:37 AM

Calculate this limit :
$\lim_{x\rightarrow 0}(\frac{1}{x}(x+1+\sqrt{x^{2}+1}-\frac{2}{x^{2}+1}))$

**tonio** · December 7th 2009, 06:22 AM

Originally Posted by dhiab

Calculate this limit :
$\lim_{x\rightarrow 0}(\frac{1}{x}(x+1+\sqrt{x^{2}+1}-\frac{2}{x^{2}+1}))$

$\lim_{x\rightarrow 0}\left(\frac{1}{x}\left(x+1+\sqrt{x^{2}+1}-\frac{2}{x^{2}+1}\right)\right)$ $=\lim_{x\to 0}\frac{x^3+x^2+(x^2+1)^{3\slash 2}+x-1}{x^3+x}=1$ , for example using L'Hospital's Rule.

Thread: limit

LinkBack

Thread Tools

Display

limit

Similar Math Help Forum Discussions

limit question on a limit comparison test problem.

use limit definition to prove that the limit is correct

[SOLVED] limit of function exists, but limit of its derivative doesn't.

Limit, Limit Superior, and Limit Inferior of a function

1. find the limit 2. use the definition of the limit to prove that

Search Tags