Problems 1-21 could be on the no Derive part. Sections 1.2, 2.2, 2.3, 3.1, 3.3, 3.4, 4.1, 4.2

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1 MTH 120 Practice Test #1 Sections 1.2, 2.2, 2.3, 3.1, 3.3, 3.4, 4.1, 4.2 Use the properties of limits to help decide whether the limit eists. If the limit eists, find its value. 1) lim 5 2) lim Give an appropriate answer. 3) Let lim f() = ) Let lim f() = Find the asymptotes of the function. 5) y = ) y = ) y = Use the properties of limits to help decide whether the limit eists. If the limit eists, find its value ) lim ) lim Find the derivative. 10) f() = , find fʹ() 11) y = ) f() = Problems 1-21 could be on the no Derive part. 13) y = ) y = 4 3 Find fʹ() at the given value of. 15) f() = ; Find f (36). 16) f() = -9 ; Find f (-6). Use the product rule to find the derivative. 17) f() = ( )( ) 18) f() = (4-2)( ) Use the quotient rule to find the derivative. t2 19) g(t) = t ) y = ) y = Write a cost function for the problem. Assume that the relationship is linear. 22) An electrician charges a fee of $55 plus $40 per hour. Let C() be the cost in dollars of using the electrician for hours. 23) Marginal cost, $150; 30 items cost $5000 to produce 24) Suppose that the demand and price for a certain model of graphing calculator are related by p = D(q) = 106-2q, where p is the price (in dollars) and q is the demand (in hundreds). Find the demand for the calculator if the price is $41. Round to the nearest whole number if necessary. 1

2 25) Let the demand and supply functions be represented by D(p) and S(p), where p is the price in dollars. Find the equilibrium price and equilibrium quantity for the given functions. D(p) = p S(p) = 160p ) A book publisher found that the cost to produce 1000 calculus tetbooks is $25,900, while the cost to produce 2000 calculus tetbooks is $50,600. Assume that the cost C() is a linear function of, the number of tetbooks produced. What is the marginal cost of a calculus tetbook? 27) A toilet manufacturer has decided to come out with a new and improved toilet. The fied cost for the production of this new toilet line is $16,600 and the variable costs are $66 per toilet. The company epects to sell the toilets for $155. Formulate a function P() for the total profit from the production and sale of toilets. 28) Regrind, Inc. regrinds used typewriter platens. The cost per platen is $2.40. The fied cost to run the grinding machine is $164 per day. If the company sells the reground platens for $4.40, how many must be reground daily to break even? 32) John owns a hotdog stand. He has found that his profit is represented by the equation P() = , where is the number of hotdogs. How many hotdogs must he sell to earn the most profit? 33) Suppose the cost of producing items is given by C() = and the revenue made on the sale of items is R() = Find the number of items which serves as a break-even point. 34) Suppose the cost per ton, y, to build an oil platform of thousand tons is approimated by y = 312,500. What is the cost for = 300? ) If the average cost per unit C() to produce units of plywood is given by C() = , what is the unit cost for 20 units? Decide whether the limit eists. If it eists, find its value. 36) lim (-1)- f() and lim (-1)+ f() 4 y 29) Midtown Delivery Service delivers packages which cost $2.30 per package to deliver. The fied cost to run the delivery truck is $325 per day. If the company charges $7.30 per package, how many packages must be delivered daily to make a profit of $75? ) A shoe company will make a new type of shoe. The fied cost for the production will be $24,000. The variable cost will be $31 per pair of shoes. The shoes will sell for $100 for each pair. How many pairs of shoes will have to be sold for the company to break even on this new line of shoes? 37) lim f() ) Bob owns a watch repair shop. He has found that the cost of operating his shop is given by C() = , where is the number of watches repaired. What is his minimum cost? 2

3 38) lim f() 0 45) y = 2-1 between = 1 and = 5 Find the instantaneous rate of change for the function at the given value. 46) s(t) = t2 + 5t at t = 4 47) f() = at = 2 39) lim f() -1/2 48) Suppose that the total profit in hundreds of dollars from selling items is given by P() = Find the marginal profit at = 1. 49) The total cost to produce handcrafted wagons is C() = Find the rate of change of cost with respect to the number of wagons produced (the marginal cost) when = 8. Graph to find the limit ) lim ) lim A) - B) C) Does not eist D) Find all points where the function is discontinuous. 42) Find the equation of the tangent line to the curve when has the given value. 50) f() = 3 4 ; = 4 51) The graph shows the total sales in thousands of dollars from the distribution of thousand catalogs. Find the average rate of change of sales with respect to the number of catalogs distributed from 10 to 50. Sales (in thousands) 43) Find the average rate of change for the function over the given interval. 44) y = between = -4 and = Number (in thousands) 3

4 Find the -values where the function does not have a derivative. 52) 61) If the price of a product is given by P() = , where represents the demand for the product, find the rate of change of price when the demand is 8. 53) 62) The profit in dollars from the sale of thousand compact disc players is P() = Find the marginal profit when the value of is 12. Write an equation of the tangent line to the graph of y = f() at the point on the graph where has the indicated value. 63) f() = ( )(-2 + 5), = 0 54) Suppose the demand for a certain item is given by D(p) = -3p2 + 7p + 7, where p represents the price of the item. Find Dʹ(5). 55) The revenue generated by the sale of bicycles is given by R() = /200. Find the marginal revenue when = 900 units. Find the slope of the line tangent to the graph of the function at the given value of. 56) y = ; = 1 57) y = 7 - ; = 4 Find an equation for the line tangent to given curve at the given value of. 58) y = ; = 5 Find all values of (if any) where the tangent line to the graph of the function is horizontal. 59) y = ) f() = , = 0 65) The total cost to produce units of perfume is C() = (8 + 2)(6 + 7). Find the marginal average cost function. 66) The demand function for a certain product is given by: D(p) = 6p p Find the marginal demand Dʹ(p). 67) The total revenue for the sale of items is given by: R() = /2. Find the marginal revenue Rʹ(). Solve the following. 60) Find all points of the graph of f() = whose tangent lines are parallel to the line y - 39 = 0. 4

5 Answer Key Testname: 120PRACTICETEST1 1) 10 2) 3 2 3) 5 4) 14 5) Vertical asymptote at = -1; horizontal asymptote at y = 3 6) No asymptotes; hole at = 6 7) Vertical asymptote at = 9 4 horizontal asymptote at y = 0 8) - 2 9) 0 10) ) dy d = ) fʹ() = - 4 3/ ) dy d = ) dy d = ) ) ) fʹ() = ) fʹ() = ) gʹ(t) = t 2-22t (t - 11)2 20) dy d = ) dy d = (7-2)2 22) C() = ) C() = ) 3250 calculators 25) $10; ) $ ) P() = ) 82 platens 29) 80 packages 30) 348 pairs 31) $171 32) 30 hotdogs 33) 8 items 34) $101,

6 Answer Key Testname: 120PRACTICETEST1 35) $ ) -2; -7 37) Does not eist 38) -2 39) -1 40) A 41) 42) = 1 43) = -2, = 0, = 2 44) 43 45) ) 13 47) 5 48) $600 per item 49) $376 per wagon 50) y = ) ) = 0 53) = 0, = 3 54) ) $ ) 30 57) ) y = ) 2, -2 60) (5, 120) 61) ) $322 63) y = ) y = ) ) Dʹ(p) = (8p + 19)2 67) Rʹ() = 50(7-1/2-2) (7 + 3/2)2 6