Canculus

TUTORIAL 3 FUNCTIONS caper 1 For f( x) = 22+ 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) bother 2 The effect N of cars produced at a certain factory in 1 day after t hours of operation is accustomed 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 backward 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 footing 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 some(prenominal) 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 causal agent an Ace Rental compact car x kilometers in a day, the company charge f(x) dollars, where Describe Ace Rentals price policy in plain English. ( Be sure to interpret the constants 30, 0. 7, and 100 that break through in the pricing formula) Problem 6 For the following demand and picture functions of a product, state the economically sensible ranges of price and total for which they atomic number 18 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 tack on 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 quint terms of the following sequences 1nn-1n12n Problem 2 study the convergence or divergence of the following sequences 1nn-1n12n 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)