Question

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

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 $x=-7$

\[
\sqrt{-7 + 11}+2=\sqrt{4}+2=2 + 2=4
\]

Answer:

4