Test Bank for Applied Calculus Brief 6th Edition by Berresford Link full download: http://testbankair.com/download/test-bank-for-appliedcalculus-brief-6th-edition-by-berresford/ Chapter Derivatives And Their Uses Complete the table and use it to predict the limit, if it exists 6x7 f ( x) x lim f (x) ? x x 0.5 f (x) 0.51 0.501 0.5001 0.5 ? 0.4999 0.499 0.49 A) –160.0 B) 80.0 C) –80.0 D) 0.5 E) does not exist Ans: C Use properties of limits and algebraic methods to find the limit, if it exists lim (8x x3 13x 3x 13) A) –121 B) 121 C) 141 D) –141 E) does not exist Ans: B Find lim x x without using a graphing calculator or making tables x x A) B) –5 C) D) E) Ans: D Berresford/Rockett, Brief Applied Calculus, 6e exists x 14 A) B) Use properties of limits and algebraic methods to find the limit, if it –7 8x lim 144x 14 14 C) 14 D) 14 E) does not exist Ans: D exists Use properties of limits and algebraic methods to find the limit, if it lim x x –5 92x 14 x 2x A) 5 B) C) D) E) exists does not Use properties of limits and algebraic methods to find the limit, if it lim 2x x 13 exist Ans: B x 32 x9 x A) 17 12 B) 17 12 C) 12 17 12 D) 17 E) does not exist Ans: B ©2013 Cengage Learning All Rights Reserved Page 38 Berresford/Rockett, Brief Applied Calculus, 6e Use properties of limits and algebraic methods to find the limit, if it exists 2 lim 9x h0 h A) xh B) 2x C) 9x D) 18x E) does not exist Ans: D A graph of y f ( x) is shown and a c-value is given For this problem, use the graph to find lim f ( x) xc c A) B) C) –6 D) –4 E) does not exist Ans: A Use properties of limits and algebraic methods to find the limit, if it exists 16 7x for x lim f (x ), where f (x) x3 A) 5xfor x C) –6 B) D) –does not5 E) exist Ans: E 10 Find lim x+6 f ( x) f ( x) x–6 + A) B) C) D) E) Ans: D –1 –6 for x+6 ©2013 Cengage Learning All Rights Reserved Berresford/Rockett, Brief Applied Calculus, 6e 11 Find lim f ( x) for the graph of f ( x) given below + x A) B) C) D) E) -3 inf Ans: A 12 Find lim– x +1 x –1 B) C) D) E) F) Ans: C –1 13 Find lim –1 + x A) B) C) D) –6 x–6 E) Ans: E ©2013 Cengage Learning All Rights Reserved Page 40 Berresford/Rockett, Brief Applied Calculus, 6e Page 39 14 For the given x-value, use the figure to determine whether the function is continuous or discontinuous at that x-value x5 A) discontinuous continuous B) Ans: A 15 Determine whether the function is continuous or discontinuous at the given x-value x if x –4 x –4 f (x ) 9x A) 123 if x –4 discontinuous continuous B) Ans: B 16 Determine whether the given function is continuous If it is not, identify where discontinuous y 3x 4x A) discontinuous at x B) discontinuous at x C) discontinuous at x5 discontinuous at x 10 E) D) Ans: E it is continuous everywhere 17 Determine whether the function is continuous or discontinuous at the given x-value x y ,x –7 x A) continuous discontinuous B) Ans: A ©2013 Cengage Learning All Rights Reserved Page 41 Berresford/Rockett, Brief Applied Calculus, 6e 18 Determine whether the given function is continuous If it is not, identify where it is discontinuous You can verify your conclusions by graphing the function with a graphing utility, if one is available y 8x 3x x 12 A) discontinuous at x B) discontinuous at x1 C) discontinuous at x D) discontinuous at x1 2 continuous everywhere E) Ans: D ©2013 Page Cengage Learning All Rights Reserved 42 Berresford/Rockett, Applied Calculus, 6e Brief P,P, and P , 19 slopes By imagining tangent lines at points state whether the are positive, zero, or negative at these points A) At P : positive slope At P2 : negative slope At P3 : positive slope B) At P : zero slope At P2 : negative slope At P3 : positive slope C) At P : zero slope At P2 : positive slope At P3 : negative slope D) At P : positive slope At P2 : positive slope At P3 : positive slope E) At P : positive slope At P2 : negative slope At P3 : negative slope Ans: C ©2013 Cengage Learning All Rights Reserved Page 43 20 Which graph represents f ( x) if the graph of f ( x) is displayed below? A) B) Berresford/Rockett, Brief Applied Calculus, 6e C) D) ©2013 Cengage Learning All Rights Reserved Page 44 Berresford/Rockett, Brief Applied Calculus, 6e 63 Find f ( x ) and f (x) 3f (x ) 5x 5x A) B) f ( x ) 15x , f (x )30x f ( x ) 30x , f (x) 30 C) f ( x ) 15x , f (x ) 30x D) f ( x ) 15x , f (x) 30 E) f ( x ) –10, f (x) Ans: A 64 Find the third derivative y 7x 5x 7x A) 42 B) 42x C) 21 D) 21x E) Ans: A 65 Find the indicated derivative (4) Find y if y x 8x 336x5 A) B) 336x C) D) 336x 48x 1680x 48x E) 1680x Ans: E 66 11 Find f ''(x) for the function x 99 B) 99 A) 299 x 92 D) C) 11 x 72 x 72 16 x 72 E) 11 x Ans: A ©2013 Cengage Learning All Rights Reserved Page 58 Berresford/Rockett, Brief Applied Calculus, 6e 67 21 Find f '''( x) for the function x A) 15 399 x2 B) 15 6783 x C) 17 399 x2 D) 6783 x 15 16 E) 17 399 x2 Ans: B 68 A)Find ( 4) f (x) for the function 9009 x 13 x B) 9009 x C) 143 x2 D) 9009 16 x 52 E) 1437 16 x Ans: D 69 Find the second 30 A) 42x4 B) x8 42 30x4 42x4 C) 30x4 D) x4 x8 Ans: C 42 x8 30 Berresford/Rockett, Brief ©2013 Cengage Learning All Rights Reserved Page 59 42x4 E) x4 42 Applied Calculus, 6e 70 Find f ''(5) for the function 4x A) 625 B) 3125 500 D) C) 500 E) Ans: C 71 Find the third derivative y x23 –120 A) x5 x5 B) 120 x C) D) x Ans: E 40 E) –120 72 2 Find the second derivative of the function (x 3)(x 7) A) 4x x 21 B) 4x3 8x C) 12 x2 20 D) 12 x E) x 20 x 21 Ans: D 73 d 37 Evaluate the expression dx x x A) B) C) D) E) Ans: 42 –42 –210 210 E ©2013 Cengage Learning All Rights Reserved 74 Page 60 Berresford/Rockett, Brief Applied Calculus, 6e Find the second derivative of the function x 2x7 56 A) B) C) (2 x 7) 112 (2 x 7) 112 (2 x 7) D) 28 (2 x 7) E) 28 (2 x 7) Ans: C 75 If the formula describing the distance s (in feet) an object travels as a function of time is the acceleration of the object when t 5? A) ft/sec t (in seconds) is s 60 90t 17t What B) –34 ft/sec C) D) –80 ft/sec2 34 ft/sec E) 80 ft/sec Ans: B 76 300 After t hours, a car is a distance s (t ) 60t t the velocity after hours A) 51 miles/hour B) 66 miles/hour C) 54 miles/hour D) 57 miles/hour E) 63 miles/hour Ans: D miles from its starting point Find 77 If f ( g ( x )) A) x x x and f (x) x , find g ( x) B) x3 C) D) x 23 x 2 3x x E) x 3x Ans: D ©2013 Cengage Learning All Rights Reserved 78 If f ( g ( x)) Page 61 x 6x and g (x ) 8x 6x , find f ( x) A) x B) 8x D) x2 1 Ans: A x 79 C) x 6x E) 12 6x 6x x4 If f (g (x )) and f (x ) x , find g ( x) x B) x x x2 C) D) x x E) x4 Ans: E 80 Find f '( x) for the given function f (x ) ( x A) x x2 1) x4 A) B) x x2 C) x x2 x x2 D) E) x x2 Ans: A ©2013 Cengage Learning All Rights Reserved Page 62 Berresford/Rockett, Brief Applied Calculus, 6e 81 Differentiate the given function y (54x) A) B) 4x 5x C) D) 5x E) 5x 20x Ans: C 82 Find the derivative of the given function Simplify and express the answer using positive exponents only (4 x x 2) y A) 27(4 x x 2) 108 x (4 x x 2) 27 x (4 x x 8x D) 2) 16 x C) 54 x (4 x x 8x B) 2 2) 16 x 5 5 E) 108 x (4 x x 2 2) 8x Ans: C 83 Differentiate the given function 14 k (x ) (5x x 6) A) 13 28(5 x x 6) 35x x 13 B) 4(5 x x 6) 35 x 6 C) 4(35x6 1)13 D) 4(5 x x 6)15 x6 E) 7 2(5 x x 12) 35 x 13 1 Ans: B ©2013 Cengage Learning All Rights Reserved Berresford/Rockett, Brief Applied Calculus, 6e 84 Differentiate the given function y x 3x 35 x43 1/ A) B) x 53x 1/ D) C) 35 x 3x 27x5 E) 12 3x 3/ 1/ x5 1/ 35 x4 x x 35 x Ans: D Page 63 85 Differentiate the given function.3 p q ( q 7) 12q2 A) q3 q B) C) 12q2 q 5 q3 3q D) 3q 4q3 E) q37 Ans: C ©2013 Cengage Learning All Rights Reserved Page 64 Berresford/Rockett, Brief Applied Calculus, 6e 86 Differentiate the given function y (7 x 1) x 17 A) B) C) 7 17 x 17 x 17 x 17 x E) 1 7 42 x 17 Ans: A 87 Differentiate the given function 7/2 y (6 x x 1) A) 6x 3x 48 x 73 B) x 83 x 48 x7 6x8 3x1 C) D) 26x8 3x1 E) 6x 3x19 6x8 3x1 48x 7 Ans: E 88 Find the derivative of the given function Simplify and express the answer using positive exponents only y4 x2 x 7x A) x 8x 40x 21x 128x 56 ©2013 Cengage Learning All Rights Reserved Page 71 D) B) C) D) x 8x 40x x 8x 40x x 8x 40x 21x 128x 56 21x 128x 56 21x 128x 56 E) x 8x 40x 21x 128x 56 Ans: E 44 Use the Generalized Power Rule to find the derivative of the function x x x 33 x A) x B) 2x4 x4 x1 4 2x C) x 3x 11 x 3 x4 D) x 2x E) 3x x Ans: E 90 Differentiate the given function y (6 x) A) B) 252 (6 x) 42 (6 x) Berresford/Rockett, Brief Applied Calculus, 6e 252 (6 x) C) D) 42 (6 x) 42 E) (6 x)5 Ans: C ©2013 Cengage Learning All Rights Reserved Page 66 Differentiate the given function y 91 x A) 12 B) x4 x5 C) 12 D) x4 E) x5 x5 Ans: D 92 A) company's cost function is C ( x ) x 800 dollars, where x is the number of units Find the marginal cost function and evaluate it for x 30 Round your answer to two decimal places A) 1.18 dollars B) 2.35 dollars C) 50.99 dollars D) 17.65 dollars E) 66.33 dollars Ans: A 93 If $1800 is deposited in a bank paying r% interest compounded annually, years later its value will be V (r ) 1800(1 0.01r) dollars Find V '(8) Round your answer to nearest cent A) 122.44 dollars B) 132.24 dollars ©2013 Cengage Learning All Rights Reserved Page 73 C) 24.49 dollars D) 26.45 dollars E) 142.82 dollars Ans: A Berresford/Rockett, Brief Applied Calculus, 6e 94 For the function displayed in the graph below, find all x-values at which the derivative does not exist A) B) –3, 0, C) D) –1, E) none Ans: B 95 For the function displayed in the graph below, find all x-values at which the derivative does not exist Berresford/Rockett, Brief Applied Calculus, 6e A) B) 0, C) none D) –1 E) –1, Ans: E 96 For the function f ( x ) ( x + 2) , find the x-value at which the derivative does not exist A) -2 B) C) D) E) none Ans: A ©2013 Cengage Learning All Rights Reserved 97 Page 68 Use the numerical derivative function on a graphing calculator to calculate the derivative of the function f ( x) at x Is the calculator correct? x A) 2; No, the calculator is not correct B) 0; Yes, the calculator is correct C) ; No, the calculator is not correct D) 0; No, the calculator is not correct E) 2; Yes, the calculator is correct Ans: D 98 If a function is continuous at a point, then it is also not defined at that same point? A) True B) False Ans: B ©2013 Cengage Learning All Rights Reserved Page 75 ... below? A) B) Berresford/ Rockett, Brief Applied Calculus, 6e C) D) ©2013 Cengage Learning All Rights Reserved Page 44 Berresford/ Rockett, Brief Applied Calculus, 6e E) Ans: C 21 For the given... (x ) 6x 2x A) –14 B) –4 C) –10 D) E) Ans: C Berresford/ Rockett, Brief Applied Calculus, 6e 27 For the function in this problem, find the derivative, by using the definition f (x ) 5x 3x A) x 23... Page 41 Berresford/ Rockett, Brief Applied Calculus, 6e 18 Determine whether the given function is continuous If it is not, identify where it is discontinuous You can verify your conclusions by graphing