1. For the following demand equation compute the elasticity of demand and determine whether the demand is elastic, unitary, or inelastic at the indicated price. (Round your answer to three decimal places.)
x=-3/4p + 29; p= 9
2. For the following demand equation compute the elasticity of demand and determine whether the demand is elastic, unitary, or inelastic at the indicated price. (Round your answer to three decimal places.)
x= -3/2p + 11; p=3
3. A passenger ship leaves port sailing east at 14 mph. Two hours later, a cargo ship leaves the same port heading north at 10 mph.
(a) Find a function giving the distance in miles between the two ships t hr after the passenger ship leaves port.
(b) How far apart are the two ships 3 hr after the cargo ship leaves port? (Round your answer to two decimal places.)
4. Find f(a + h) - f(a) for the function. Simplify your answer. f(x) = x2 - 15x + 7
5. A rectangular box is to have a square base and a volume of 40 ft3. The material for the base costs 40 cents/ft2, the material for the sides costs 10 cents/ft2, and the material for the top costs 24 cents/ft2. Letting xdenote the length of one side of the base, find a function in the variable x giving the cost (in dollars) of constructing the box.
6. In the pair of supply and demand equations below, where x represents the quantity demanded in units of a thousand and p the unit price in dollars, find the equilibrium quantity and the equilibrium price.
p = -x2 - 3x + 92 and p = 7x + 17
7. Find the indicated limit. limx→1 (2x3 - 5x2 + x + 3)
8. Find the indicated one-sided limit, if it exists. (If an answer does not exist, enter DNE.)
limx→1+ (X+ 10)/(X+1)
9. Find the average cost function C associated with the following total cost function C. a) C(x) = 0.000008x3 - 0.1x2 + 110x + 59000
b) What is the marginal average cost function C'?
c) Compute the following values. (Round your answers to three decimal places.)