Question

1. evaluate

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

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:

$8$