MATH CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #3 - FALL DR. DAVID BRIDGE

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1 MATH CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #3 - FALL DR. DAVID BRIDGE MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use a calculator to estimate the limit. 1) lim A) 4 B) Does not eist C) 8 D) 64 2) lim 1-1 ( - 1)2 A) Does not eist B) 1 C) D) 0 3) lim A) B) C) Does not eist D) ) lim 0 e 3-1 A) 3e 3 B) 3 C) 0 D) Does not eist 5) lim ln - ln 3-3 A) Does not eist B) 0 C) 1 3 D) 3 Use the limit properties to find the following limit. 6) If lim f() = 9 and lim g() = 3, find lim [f() - g()]. A) 12 B) 3 C) 0 D) 6 7) If lim 4 f() = 3 and lim 4 g() = 7, find lim 4 [f() g()]. A) Does not eist B) 21 C) 84 D) 10 8) If lim f() = 16 and lim g() = 2, find lim f() g(). A) Does not eist B) 24 C) 3 D) 8 9) If lim A) f() = 6 and lim g() = 13, find lim f() + g(). 5g() B) 3 C) D) 19 18

2 Use the properties of limits to evaluate the limit if it eists. 10) lim A) B) C) Does not eist D) 0 11) lim A) 5 B) -1 C) 0 D) Does not eist 12) lim A) 0 B) -8 C) Does not eist D) 5 Find the average rate of change for the function over the given interval. 13) y = between = 6 and = 8 A) 23 B) 68 C) 17 D) ) y = 2 between = 2 and = 8 A) 1 3 B) C) 7 D) 2 15) y = 3 between = 4 and = 7-2 A) 1 3 B) C) 2 D) 7 The graph shows the total sales in thousand of dollars from the distribution of thousand catalogs. Find the average rate of change of sales with respect to the number of catalogs distributed for the change in. 16) 10 to 20 A) 3 2 B) 2 C) 1 D) ) 10 to 40 A) 1 4 B) 2 3 C) 1 3 D) 4

3 Solve the problem. 18) Compute the instantaneous rate of change of the function at at = a. f() = 2 + 3, a = 4. A) 8 B) 11 C) 12 D) -8 19) Compute the instantaneous rate of change of the function at at = a. f() = , a = -3. A) 20 B) -20 C) 14 D) 21 20) The position of a particle moving on a number line at time t is given by s(t). Find the instantansous velocity at time t = t 0 s(t) = 2t2 + 7t + 2; t0 = 5 A) 27 B) 7 C) -27 D) -7 Find the equation of the tangent line to the curve when has the given value. 21) f() = ; = 4 A) y = B) y = C) y = D) y = ) f() = 4 ; = 5 A) y = B) y = C) y = D) y = ) f() = 5 ; = 4 A) y = B) y = C) y = D) y = Find the point from those given that has the given property. 24) The point where the slope of the tangent is greatest 10 y A) (2,6) B) (0,0) C) (-2,-2)

4 25) The point where the slope of the tangent is greatest 10 y A) (2,-6) B) (0,0) C) (-2,2) 26) The point where the slope of the tangent is least 10 y A) (0,2) B) (-1,-5) C) (1,3) 27) The point where the slope of the tangent is least 10 y A) (1.68,-0.35) B) (-0.84,-1.42) C) (0.84,-1.42) Solve the problem. 28) The total cost to produce handcrafted wagons is C() = Find the marginal cost when = 8. A) 2632 B) 946 C) 1066 D) ) The profit in dollars from the sale of thousand compact disc players is P() = Find the marginal profit when the value of is 7. A) $72 B) $112 C) $66 D) $118

5 Find the derivative. 30) f() = A) 8-2 B) 4-2 C) 42-2 D) ) y = A) B) C) D) ) f() = 97/ A) / B) / C) /5-10 D) / ) f() = 8 ; ( > 0) A) 7(7 ) B) /8 C) 9 8 9/8 D) 1 8-7/8 34) f() = (5-5) A) f'() = 3.331/2-5-1/ B) f'() = 3.331/ / C) f'() = 7.51/2-5-1/ D) f'() = 7.51/ / Find the following. 35) f'(16) if f() = 43/2-51/2 A) B) C) D) ) f'(1) if f() = A) -2 B) 2 C) 8 D) -8 37) f'(4) if f() = 7 - A) B) C) 3 16 D) Solve the problem. 38) Suppose the demand for a certain item is given by D(p) = -3p2 + 6p + 6, where p represents the price of the item. Find D'(p), the rate of change of demand with respect to price. A) D'(p) = -3p2 + 6 B) D'(p) = -6p + 6 C) D'(p) = -6p2 + 6 D) D'(p) = -3p ) Suppose the demand for a certain item is given by D(p) = -3p2 + 6p + 6, where p represents the price of the item. Find D'( 6). A) -24 B) 6 C) 0 D) -30

6 40) The revenue generated by the sale of bicycles is given by R() = Find the marginal revenue when 200 = 1000 units. A) $10.00/unit B) $20.00/unit C) $100.00/unit D) $0.00/unit Find the derivative of the function. 41) f() = (4-4)(6 + 1) A) f'() = B) f'() = C) f'() = D) f'() = ) f() = ( )( ) A) f'() = B) f'() = C) f'() = D) f'() = ) Suppose p(5) = 6, p (5) = 7, q(5) = 8, and q (5) = 9. Let f() = p()q(). Find f (5). A) f () = -30 B) f () = 110 C) f () = -2 D) f () = ) f() = (6 + 5)2 A) f'() = B) f'() = C) f'() = D) f'() = Use the quotient rule to find the derivative. 1 45) f() = A) f'() = - 1 (77 + 2)2 B) f'() = 76 (7 + 2)2 C) f'() = 1 (77 + 2)2 76 D) f'() = - (7 + 2)2 46) g(t) = t2 t - 11 A) g'(t) = t 2-22t (t - 11)2 B) g'(t) = t2 (t - 11)2 C) g'(t) = 22t (t - 11)2 D) g'(t) = t t (t - 11)2 47) y = A) y' = ( )2 B) y' = ( )2 C) y' = 42-8 ( )2 D) y' = ( )2 Solve the problem. 48) The total cost to produce units of perfume is C() = (4 + 4)(5 + 4). Find the marginal average cost function. A) B) C) D)

7 49) The total profit (in hundreds of dollars) from selling items is given by P() = Find the marginal average profit 6-4 function. A) C) -14 (6 + 1)2 hundreds of dollars per item B) (62-4) 2 hundreds of dollars per item -2 (6 + 1)2 hundreds of dollars per item D) (62-4) 2 hundreds of dollars per item 50) A particle is moving on a horizontal line. Its distance from the origin at time t seconds is f(t) = the instantaneous velocity at 2 seconds? A) ft/sec B) - 5 ft/sec C) t feet. What is t2+ 1 ft/sec D) ft/sec Find the location and value of each relative etremum for the function. 51) A) (-3,-1), (-2,0), (2,1) B) (-3,-1), (-1,2), (-2,0) C) (-3,-1), (-1,2), (2,1) D) (-2,0), (-1,2), (2,1) 52) A) (-2, 3), (2, 0) B) None C) (2, 0) D) (-2, 3) 53) A) (1.5, -1) B) (-6, 3), (1.5, -1), (4.2, 2) C) (-6, 3), (4.2, 2) D) None

8 Identify the intervals where the function is changing as requested. 54) Increasing A) (-2, 2) B) (-3, ) C) (-3, 3) D) (-2, ) 55) Increasing A) (3, 6) B) (-2, 0) C) (3, ) D) (-2, ) 56) Decreasing A) (6, 12) B) (5, 1) C) (5, 12) D) (6, 1) 57) Decreasing A) (-, -2) B) (-, 3) C) (0, 3) D) (0, -2) Find the largest open interval where the function is changing as requested. 58) Increasing y = 7-5 A) (-, ) B) (-5, ) C) (-, 7) D) (-5, 7) 59) Increasing f() = A) (-1, 1) B) (-, ) C) (-, -1) D) (1, )

9 1 60) Increasing f() = A) (1, ) B) (0, ) C) (-, 1) D) (-, 0) 61) Decreasing f() = A) (-3, ) B) (-, -3) C) (-, 3) D) (3, ) 62) Decreasing f() = 3-4 A) 2 3 3, B) , C) (-, ) D) -, Evaluate f''(c) at the point. 63) f() = (2-6)(3-6), c = 1 A) f''(1) = 16 B) f''(1) = -28 C) f''(1) = -16 D) f''(1) = 24 Solve the problem. 64) Find the acceleration function a(t) if s(t) = -3t3 + 7t2-8t + 3. A) a(t) = -18t + 14 B) a(t) = -9t2-8t + 14 C) a(t) = -18t - 8 D) a(t) = -9t2 + 14t - 8 s is the distance (in ft) traveled in time t (in s) by a particle. Find the velocity and acceleration at the given time. 65) s = 3t3 + 3t2 + 9t + 9, t = 2 A) v = 24 ft/s, a = 30 ft/s2 B) v = 57 ft/s, a = 42 ft/s2 C) v = 30 ft/s, a = 24 ft/s2 D) v = 42 ft/s, a = 57 ft/s2 Find the largest open intervals where the function is concave upward. 66) f() = A) (-, -1) B) (-1, ) C) None D) (-, ) 67) f() = A) -, B) , C) -, 4 4 D) 15 4, 68) f() = 6 A) (-, ) B) (0, ), (-, 0) C) (-, 0) D) (0, ) 69) f() = 4-63 A) (-, 0) B) (-, 0), (3, ) C) (-, ) D) (0, 3) Evaluate. 70) 3 d A) C B) C C) C D) C

10 71) 42/3 d A) 8 3 5/3 + C B) 4 3 5/3 + C C) /3 + C D) 65/3 + C 72) 5-3 d A) C B) C C) + 5C D) ) 5 3 d A) 5 4 4/3 + C B) 154/3 + C C) 54/3 + C D) /3 + C 74) (72-4) d A) C B) C C) C D) C 75) ( ) d A) C B) C C) C D) C 76) ( ) d A) C B) C C) C D) C Evaluate the integral. 77) -1 ( ) d -3 A) B) 18.5 C) D) ) 79) d 1 A) 3.45 B) -3.5 C) D) /2 d 1 A) 3.4 B) 2.8 C) 5.67 D) 4.67

11 80) 4 (3/2 + 1/2 - -1/2) d 1 A) B) C) 46 D) 14.93

12 Answer Key Testname: MATH PRACTICE EXAM #3 1) C 2) A 3) D 4) B 5) C 6) D 7) B 8) D 9) A 10) A 11) B 12) B 13) D 14) A 15) B 16) C 17) B 18) B 19) C 20) A 21) B 22) D 23) C 24) A 25) C 26) C 27) B 28) B 29) C 30) A 31) C 32) D 33) D 34) D 35) C 36) B 37) D 38) B 39) D 40) D 41) D 42) B 43) B 44) B 45) D 46) A 47) B 48) C 49) D 50) D 51) C 52) A 53) B 54) A 55) C 56) C 57) B 58) A 59) D 60) D 61) A 62) B 63) B 64) A 65) B 66) D 67) D 68) D 69) B 70) C 71) C 72) B 73) D 74) C 75) A 76) C 77) C 78) A 79) D 80) B