Limit $\lim \limits_{x \to 2}{\frac{\sqrt{x^3 - 3x^2 + 4}-x +2}{x^2 - 4}}$ I try to calculate $\lim \limits_{x \to 2}{\frac{\sqrt{x^3 - 3x^2 + 4}-x +2}{x^2 - 4}}$. So, $\frac{\sqrt{x^3 - 3x^2 + 4}-x +2}{x^2 - 4} = \frac{(x-2)x}{(x+2)(x+\sqrt{(x-2)^2(x+1)}-2)}$ but I don't know what to do next.

No L'Hospital, too messy. You are almost there, rewrite the expression as 
$$
\frac{(x-2)x}{(x+2)(x-2)(1 +\sqrt{\frac{(x-2)^2(x+1)}{(x-2)^2}}}
$$
what do you get? 
