Calculus Answers

Suppose that the utility function for two products is given by U = x²y, and the budget constraint is 2x + 3y = 120. Find the values of x and y that maximize utility.

Suppose that the utility function for two

commodities is given by U = x² y³ and the budget constraint is 10x + 15y = 250. Find the values of x and y that maximize utility 

Trace the curve y=x³-x

Sketch the region enclosed by the curves and find its area.

y=e^x, y=e^8x, x=0, x=ln2

The equation N(t) = 600/1 + 49e^0.7t models the number of people in a town who have heard a rumor after t days. As t increases without bound, what value does N(t) approach? Interpret your answer.

How many people started the rumor?   

N(t) approaches  number?

N(t)

 is limited by the number of poeple who started the rumor.

N(t)

 is limited by the carrying capacity of the town.

N(t)

 is limited by the rate at which the rumor spreads.

N(t)

 is limited by the number of days it takes for the entire population to hear the rumor.

N(t)

 is not limited by any value and increases without bound.

. Given market demand Qd = 50 - P, and market supply P = Qs + 5

A) Find the market equilibrium price and quantity?

B) What would be the state of the market if market price was fixed at Birr 25 per unit?

C) Calculate and interpret price elasticity of demand at the equilibrium point.

The demand for tickets to an Ethiopian Camparada film is given by D(p)= 200,000-

10,000p, where p is the price of tickets.If the price of tickets is 12 birr, calculate price

elasticity of demand for tickets and draw the demand curve

Sketch the graph of the function, f defined by

f(x)= |x-3| +[x], x ∈ [2,4] where [x] is greater integer function