Chapter 9.2, Problem 51E

Electrical usage costs The monthly charge in dollars for x kilowatt-hours (kWh) of electricity used by a residential consumer of Excelsior Electric Membership Corporation from November through June is given by the function

$C(x)=\{\begin{array}{l}20+0.188x\text{ if 0}\le x\le 100\\ 38.80+0.15(x-100)\text{ if 100<}x\le 500\\ 98.80+0.10(x-500)\text{ if }x>50\end{array}$

(a) What is the monthly charge if 1100 kWh of electricity is consumed in a month?

(b) Find $\underset{x\to 100}{\lim }C(x)and\underset{x\to 500}{\lim }C(x)$, if the limits exist.

(c) Is C continuous at x = 100 and at x = 500?