### Canculus

TUTORIAL 3: FUNCTIONS Problem 1: For f( x) = 2×2+ 5x+3 and g(x) = 4x+1 find the following a) (f+g)(x) b) (f-g)(x) c) (f. g)(x) d) (f/g)(x) e) f0g(x) Problem 2: The number N of cars produced at a certain factory in 1 day after t hours of operation is given by N(t) = l00t- 5t2, 0? t? 10. If the cost C (in dollars) of producing N cars is C(N) = 15,000 + 8,000N, find the cost C as a function of the time t of operation of the factory. Problem 3: Find the inverse of the following functions. a) f(x) = 2x-3 ) f(x) = x3-1 c) f(x) = x2-1 Graph f, f-1 , and y = x on the same coordinate axes. Problem 4: The price p, in dollars, of a Honda Civic DX Sedan that is x years old is given by p(x) = 16,630(0. 90)x a) How much does a 3-year-old Civic DX Sedan cost? b) How much does a 9-year-old Civic DX Sedan cost? Problem 5: When you drive an Ace Rental compact car x kilometers in a day, the company charge f(x) dollars, where Describe Ace Rental’s pricing policy in plain English. (Be sure to interpret the constants 30, 0. 7, and 100 that appear in the pricing formula) Problem 6: For the following demand and supply functions of a product, state the economically sensible ranges of price and quantity for which they are defined. Draw the market diagram for this product. What are the equilibrium price and quantity? QD = 16 – 2p QS = -4 + 3p Problem 7: Consider the following demand and supply functions for a product. q = 500 -10p and q = -100+5p a) Find the inverse demand function and the inverse supply function. b) Draw the market diagram for this product. c) Find the equilibrium price and quantity. TUTORIAL 4: SEQUENCES, SERIES, LIMITS

Problem 1: Write down the first five terms of the following sequences 1n;n-1n;12n Problem 2: Determine the convergence or divergence of the following sequences 1n;n-1n;12n Problem 3: Compute the following limits 1)limn>? n2-2n+32n2-1 2)limn>? -2n+32n2-1 3)limn>? (n+25-n) Problem 4: Determine the convergence or divergence of the following series. 1)n=1? 25n-1 2) n=1? 1n3n 3) n=1? 13n Problem 5: Determine the sum of the following geometric series, when they are convergent. 1)1+16+162+163+…. 2)1+123+126+129+…. 3)132-134+136 – …. 4)1+326+3462+3663+…. Problem 6: 29(577) Problem 7: 33(577)