$$\lim_{x\to16}\frac{98 - 2x}{7 - \sqrt{x}}$$

Question

Accepted Answer

# Explanation:
## Step1: Rationalize the denominator
Multiply the numerator and denominator by $7 + \sqrt{x}$.
$$
\begin{align*}
&\lim_{x
ightarrow16}\frac{(98 - 2x)(7+\sqrt{x})}{(7-\sqrt{x})(7 + \sqrt{x})}\
=&\lim_{x
ightarrow16}\frac{(98 - 2x)(7+\sqrt{x})}{49 - x}
\end{align*}
$$
Factor out $2$ from the numerator: $\lim_{x
ightarrow16}\frac{2(49 - x)(7+\sqrt{x})}{49 - x}$

## Step2: Simplify the expression
Cancel out the common factor $(49 - x)$ (since $x
eq49$ as $x
ightarrow16$): $\lim_{x
ightarrow16}2(7+\sqrt{x})$

## Step3: Substitute $x = 16$
$$
\begin{align*}
&2(7+\sqrt{16})\
=&2(7 + 4)\
=&2\times11\
=&22
\end{align*}
$$

# Answer:
$22$

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QUESTION IMAGE

Question

Explanation:

Step1: Rationalize the denominator

Step2: Simplify the expression

Step3: Substitute \(x = 16\)

Answer: