4. evaluate
lim_{x
ightarrow16}\frac{16 - x}{4-sqrt{x}}

Question

4. evaluate
 lim_{x
ightarrow16}\frac{16 - x}{4-sqrt{x}}

Accepted Answer

# Explanation:
## Step1: Rationalize the denominator
Multiply numerator and denominator by $4 + \sqrt{x}$.
$$
\begin{align*}
\lim_{x
ightarrow16}\frac{16 - x}{4-\sqrt{x}}\times\frac{4+\sqrt{x}}{4+\sqrt{x}}&=\lim_{x
ightarrow16}\frac{(16 - x)(4+\sqrt{x})}{16 - x}
\end{align*}
$$
## Step2: Simplify the expression
Cancel out the common factor $(16 - x)$ (since $x
eq16$ when taking the limit).
$$
\begin{align*}
\lim_{x
ightarrow16}\frac{(16 - x)(4+\sqrt{x})}{16 - x}&=\lim_{x
ightarrow16}(4+\sqrt{x})
\end{align*}
$$
## Step3: Substitute the value of $x$
Substitute $x = 16$ into $4+\sqrt{x}$.
$$
\begin{align*}
4+\sqrt{16}&=4 + 4=8
\end{align*}
$$
# Answer:
$8$

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QUESTION IMAGE

Question

Explanation:

Step1: Rationalize the denominator

Step2: Simplify the expression

Step3: Substitute the value of $x$

Answer: