question evaluate the limit: $lim_{x
ightarrow - 7}\frac{x + 7}{sqrt{x + 11}-2}$ answer dne

Question

Accepted Answer

# Answer:
4
# Explanation:
## Step1: Rationalize the denominator
Multiply the numerator and denominator by $\sqrt{x + 11}+2$.
$$
\begin{align*}
&\lim_{x
ightarrow - 7}\frac{x + 7}{\sqrt{x + 11}-2}\times\frac{\sqrt{x + 11}+2}{\sqrt{x + 11}+2}\
=&\lim_{x
ightarrow - 7}\frac{(x + 7)(\sqrt{x + 11}+2)}{(x + 11)-4}\
=&\lim_{x
ightarrow - 7}\frac{(x + 7)(\sqrt{x + 11}+2)}{x+7}
\end{align*}
$$
## Step2: Simplify the expression
Cancel out the common factor $(x + 7)$ (since $x
eq - 7$ when taking the limit).
$$
\lim_{x
ightarrow - 7}(\sqrt{x + 11}+2)
$$
## Step3: Substitute $x=-7$
$$
\sqrt{-7 + 11}+2=\sqrt{4}+2=2 + 2=4
$$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Rationalize the denominator

Step2: Simplify the expression

Step3: Substitute $x=-7$

Answer: