Chapter 2.1, Problem 99E

Voter turnout. Statisticians often use piecewise-defined functions to predict outcomes of elections. For the following functions f and g, find the limit of each function as x approaches 5 and as x approaches 10.

$\begin{array}{l}f(x)=\{\begin{array}{ll}\begin{array}{l}0\hfill \\ 0.8-0.08x\hfill \\ 0\hfill \end{array}\hfill & \begin{array}{l}\text{if}x\le 5\hfill \\ \text{if}5<x<10\hfill \\ \text{if}10\le x\hfill \end{array}\hfill \end{array}\\ g(x)=\{\begin{array}{ll}\begin{array}{l}0\hfill \\ 0.8x-0.04x^2-3\hfill \\ 1\hfill \end{array}\hfill & \begin{array}{l}\text{if}x\le 5\hfill \\ \text{if}5<x<10\hfill \\ \text{if}10\le x\hfill \end{array}\hfill \end{array}\end{array}$