<s>[INST] 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.
 [/INST] HINT: Take $x=t+2$ and take limit as $t\to 0$ also notice that $\sqrt{t^2}=|t|$ and than take $\lim_{t\to0^+}$ and $\lim_{t\to 0^-}$
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