Math 103. Homework 3. Due 2/20/02

1. The Ace Truck Leasing Co. leases a certain size truck at $30/day and $.15/mile, whereas the Acme Truck leasing Co. leases the same size truck at $25/day and $.20/mile.

(a) Find the daily cost of leasing from each company as a function of the number of miles driven and sketch the graph of these functions.
(b) Which company should you rent a truck from for 1 day if you plan to drive 70 miles and wish to minimize cost?

2. The supply function for certain car model is given by p=(0.1)x²+(0.5)x+15, where x is the quantity supplied (in thousands) and p is the unit price (in thousand dollars). What unit price will induce the supplier to make 5,000 cars available in the market place?

If the demand function for this particular car model is given by p=(0.7)x+(14.9), what are the equilibrium quantity and equilibrium price?

3. Sketch the graph of the following function f(x) and evaluate the limit lim_{x® 1} f(x), if it exists.

f(x)= ì ï í ï î x if x < 1, 0 if x=0 2-x if x > 1

4. Find the limit

lim x® 1  x3+1 2x3+2

5. Find the limit, if it exists,

lim x® 1  x x-1