Question

Solve lim (sqrt(x^2+3) +2x) / x+1 . x->-1

Answer 1

Use l'Hospital's rule.
\[\lim_{x \rightarrow -1} \frac{\sqrt{x^2+3}}{x+1} = \lim_{x \rightarrow -1}\frac{\frac{2x}{2\sqrt{x^2+3}}}{1} = \lim_{x \rightarrow -1} \frac{x}{\sqrt{x^2+3}} = \frac{-1}{2}\]