QuestionFind the limit: $$\lim _{x \rightarrow 2} \frac{2-x}{\sqrt{x+2}-2}$$ and simplify to $$\lim _{x \rightarrow 2}(\sqrt{x+2}+2 x)$$.

Studdy Solution
Now, we simplify the second limit expression. Substitute $x =2$ into the expression.
$$\lim{x \rightarrow2}(\sqrt{x+2}+2 x) = \sqrt{2+2} +2 \times2 =2\sqrt{2} +4$$So, the simplified expressions for the given limit problems are $-2\sqrt{2} -2$ and $2\sqrt{2} +4$ respectively.