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}$