question evaluate the limit: $lim_{x\rightarrow - 15^{+}}\frac{2x + 30}{sqrt{x + 15}}$

Answer:

$2\sqrt{30}$

Explanation:

Step1: Factor out the numerator

Factor out 2 from $2x + 30$ to get $2(x + 15)$. So the limit becomes $\lim_{x\rightarrow - 15^{+}}\frac{2(x + 15)}{\sqrt{x + 15}}$.

Step2: Simplify the expression

Cancel out the common factor. Since $x\rightarrow - 15^{+}$, $x+15>0$. We can rewrite the expression as $\lim_{x\rightarrow - 15^{+}}2\sqrt{x + 15}$.

Step3: Evaluate the limit

Substitute $x=-15$ into $2\sqrt{x + 15}$. We get $2\sqrt{-15 + 15+}=2\sqrt{0+}=2\sqrt{30}$.