Single Variable Calculus, Chapter 2, Review Exercises, Section Review Exercises, Problem 13

Determine $\displaystyle \lim \limits_{s \to 16} \frac{4 - \sqrt{s}}{s - 16}$



$
\begin{equation}
\begin{aligned}

\lim \limits_{s \to 16} \frac{4 - \sqrt{s}}{s - 16} \cdot \frac{4 + \sqrt{s}}{4 + \sqrt{s}}
&= \lim \limits_{s \to 16} \frac{16 - s}{(s - 16)(4 + \sqrt{s})}
&& \text{Multiply both numerator and denominator by $(\sqrt{4} + \sqrt{s})$}\\
\\
&= \lim \limits_{s \to 16} \frac{-1\cancel{(s - 16)}}{\cancel{(s - 16)}(4 + \sqrt{s})}
&& \text{Factor numerator and cancel out like terms}\\
\\
&= \frac{-1}{4 + \sqrt{16}} = \frac{-1}{4 + 4}
&& \text{Substitute value of $s$ and simplify}\\
\\
& \fbox{$= \displaystyle \frac{-1}{8}$}

\end{aligned}
\end{equation}
$