question evaluate the limit: $lim_{x
ightarrow - 3}\frac{sqrt{x + 7}-2}{-5x - 15}$ answer

Question

Accepted Answer

# Explanation:
## Step1: Rationalize the numerator
Multiply the fraction by $\frac{\sqrt{x + 7}+2}{\sqrt{x + 7}+2}$.
$$
\begin{align*}
&\lim_{x
ightarrow - 3}\frac{\sqrt{x + 7}-2}{-5x - 15}\times\frac{\sqrt{x + 7}+2}{\sqrt{x + 7}+2}\
=&\lim_{x
ightarrow - 3}\frac{(x + 7)-4}{(-5x - 15)(\sqrt{x + 7}+2)}\
=&\lim_{x
ightarrow - 3}\frac{x + 3}{-5(x + 3)(\sqrt{x + 7}+2)}
\end{align*}
$$
## Step2: Simplify the fraction
Cancel out the common factor $(x + 3)$ (since $x
eq - 3$ when taking the limit).
$$
\begin{align*}
&\lim_{x
ightarrow - 3}\frac{x + 3}{-5(x + 3)(\sqrt{x + 7}+2)}\
=&\lim_{x
ightarrow - 3}\frac{1}{-5(\sqrt{x + 7}+2)}
\end{align*}
$$
## Step3: Substitute $x=-3$
$$
\begin{align*}
&\frac{1}{-5(\sqrt{-3 + 7}+2)}\
=&\frac{1}{-5(2 + 2)}\
=&-\frac{1}{20}
\end{align*}
$$
# Answer:
$-\frac{1}{20}$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Rationalize the numerator

Step2: Simplify the fraction

Step3: Substitute $x=-3$

Answer: