## Sunday, September 15, 2019

### Canculus

TUTORIAL 3: FUNCTIONS Problem 1: For f( x) = 2Ãƒâ€"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 RentalÃ¢â‚¬â„¢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 Ã¢â‚¬â€œ 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, LIMITSProblem 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 followin g 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+Ã¢â‚¬ ¦. 2)1+123+126+129+Ã¢â‚¬ ¦. 3)132-134+136 Ã¢â‚¬â€œ Ã¢â‚¬ ¦. 4)1+326+3462+3663+Ã¢â‚¬ ¦. Problem 6: 29(577) Problem 7: 33(577)