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