question
evaluate the limit: $lim_{x
ightarrow12}\frac{x - 12}{sqrt{x + 13}-5}$
answer

Question

Accepted Answer

# Answer:
10
# Explanation:
## Step1: Rationalize the denominator
Multiply numerator and denominator by $\sqrt{x + 13}+5$.
$$
\begin{align*}
&\lim_{x
ightarrow12}\frac{x - 12}{\sqrt{x + 13}-5}\times\frac{\sqrt{x + 13}+5}{\sqrt{x + 13}+5}\
=&\lim_{x
ightarrow12}\frac{(x - 12)(\sqrt{x + 13}+5)}{(x + 13)-25}\
=&\lim_{x
ightarrow12}\frac{(x - 12)(\sqrt{x + 13}+5)}{x - 12}
\end{align*}
$$
## Step2: Simplify the expression
Cancel out the common factor $(x - 12)$.
$$
\begin{align*}
&\lim_{x
ightarrow12}\frac{(x - 12)(\sqrt{x + 13}+5)}{x - 12}\
=&\lim_{x
ightarrow12}(\sqrt{x + 13}+5)
\end{align*}
$$
## Step3: Evaluate the limit
Substitute $x = 12$ into $\sqrt{x + 13}+5$.
$$
\begin{align*}
&\sqrt{12+13}+5\
=&\sqrt{25}+5\
=&5 + 5\
=&10
\end{align*}
$$

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QUESTION IMAGE

Question

Explanation:

Step1: Rationalize the denominator

Step2: Simplify the expression

Step3: Evaluate the limit

Answer: