Calculus for Business Economics Life Sciences and Social Sciences 13th Edition Barnett SOLUTIONS MANUAL Full download at:

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1 Calculus for Business Economics Life Sciences and Social Sciences 1th Edition Barnett TEST BANK Full download at: Calculus for Business Economics Life Sciences and Social Sciences 1th Edition Barnett SOLUTIONS MANUAL Full download at: MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. x 1) Given that f(x) =, find f -. Express the answer as a simplified fraction. 7 - x 5 A) 9 B) 9 C) - 9 D) - 9 The graph of a function f is given. Use the graph to answer the question. ) Use the graph of f given below to find f(-10) A) -10 B) 0 C) 6 D) 16-10

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3 Use the graph to evaluate the indicated it and function value or state that it does not exist. ) Find f(x) and f(0). x 0 10 y x - A) 0; 6 B) 0; does not exist C) Does not exist; 6 D) 6; 0 ) Find f(x) and x 0 - f(x). x y x A) 5; -1 B) -1; 5 C) Does not exist; does not exist D) 5; Does not exist Find the it, if it exists. 5) Find: 6x + 5 A) 1 x -1 5x - 6 B) 1 11 C) -11 D)

4 6) Given f(x) = - and g(x) = 5, find [g(x) - f(x)]. x x x - f(x) A) - 8 B) 7 8 C) D) 8 7) Find: x - A) 16 B) 8 C) -8 D) - x - 16 x + 8) Find: x - 5 x 5 x - 5 A) -1 B) 1 C) 0 D) Does not exist 9) Find: x A) 10 B) C) D) Does not exist x - 10) Find: x x - x x x + 7 x - A) 1 B) - 1 C) 0 D) Does not exist

5 11) Given f(x) = and g(x) = -5, find f(x) + g(x). x 5 x 5 x 5 f(x) A) B) 7 1 C) D) ) Evaluate the following it 1 x x - A) B) C) - D) Does not exist 1) Let f(x) = x - x Find A) - B) 5 C) -7 x + D) Does not exist 1) Let f(x) = Find x 0 A) - B) C) x - 16 x + if x > 0 x - 16 if x < 0 x - f(x). D) Does not exist x - f(x).

6 15) Let f(x) = Find A) 0 B) - C) x 0+ x - 16 x + x - 16 x - f(x) if x > 0 if x < 0 D) Does not exist 16) Let f(x) = x - 16 x + x - 16 x - if x > 0 if x < 0 Find f(x). x 0 A) - B) - C) 0 D) Does not exist 17) Evaluate the following it. 1 x + x - A) B) - C) D) Does not exist Sketch a possible graph of a function that satisfies the given conditions.

7 18) f(1) = ; f(x) = ; x 1 - x 1 + f(x) = 5 f(x) x A) 5 1 f(x) x B) 5 1 f(x) x

8 C) 5 1 f(x) x D) 5 1 f(x) x -1 19) f(0) = 6; x 0 - f(x) = 0; x 0 + f(x) = 0 5 f(x) x

9 A) y x - - B) y x - - C) y x - -

10 D) y Find the it, if it exists. 0) Find: h 0 A) 1 B) -1 C) x - - D) Does not exist f(7 + h) - f(7) for f(x) = -x + 1. h Solve the problem. 1) A company training program determines that, on average, a new employee can do P(x) pieces of work per day after s days of on-the-job training, where P(x) = x. Find P(x). x + 5 x 5 A) 105 B) 0 C) D) Does not exist ) The cost of manufacturing a particular videotape is C(x) = x, where x is the number of tapes produced. The average cost per tape, denoted by C(x), is found by dividing C(x) by x. Find C(x). x 9000 A) 10 B) 1 C) 6 D) Does not exist

11 Use the given graph to find the indicated it. ) 1 f(x) x Find f(x). x A) B) C) - D) ) 1 f(x) x Find f(x). x - A) B) - C) D)

12 5) y -8-8 x - f(x) x + - A) B) - C) D) 0 6) y -8-8 x - x 5 - A) 5 f(x) - B) C) - D) 0

13 Find the it. 7) Determine the it. x f(x), where f(x) = 1 x + 10 A) - B) 0 C) -1 D) 8) Determine the it. x 5 + f(x), where f(x) = A) - B) - C) 5 D) x (x - 5) Provide an appropriate response. 9) If the it at infinity exists, find the it. x 5x + 7x - 9-6x + A) B) - 9 C) D) 0 0) If the it at infinity exists, find the it. x A) 0 B) C) D) 1 x + 5x x + 10x +

14 Use - or where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes. x 1) g(x) = 6 - x A) x 6 - B) x 6 - C) x 6 - D) x 6 - f(x) = - ; f(x) = - ; f(x) = ; f(x) = ; x 6 + x 6 + f(x) = - ; x = 6 is a vertical asymptote x 6 + x 6 + f(x) = ; x = 6 is a vertical asymptote f(x) = - ; x = 6 is a vertical asymptote f(x) = - ; x = 0 is a vertical asymptote ) f(x) = x - 16 x + 16 A) f(x) = ; x - x + f(x) = - ; x = is a vertical asymptote B) No zeros of denominator; no vertical asymptotes C) x - - f(x) = ; x - + f(x) = - ; x = - is a vertical asymptote D) x - f(x) = ; x + f(x) = ; x = 0 is a vertical asymptote Describe the end behavior of the function. ) f(x) = 5x + 5x + 11 A) f(x) = - ; x B) x C) x D) x f(x) = - ; f(x) = ; f(x) = ; x - x - x - x - f(x) = f(x) = - f(x) = - f(x) = Provide an appropriate response. ) Find the vertical asymptote(s) of the graph of the given function. f(x) = x - 9 5x + 0 A) x = -6 B) y = - C) x = -8 D) y = 8

15 5) Find the vertical asymptote(s) of the graph of the given function. f(x) = x (x - 9)(x + ) A) x = 10, x = -10 B) x = 9, x = - C) y = 9, y = - D) x = -9 6) Find the horizontal asymptote, if any, of the given function. (x- )(x + ) f(x) = x - A) y = 1 B) x =, x = - C) y =, y = - D) None 7) Find the horizontal asymptote, if any, of the given function. f(x) = x - x - 9 9x - 5x + A) y = 5 B) y = 9 C) y = 0 D) None Solve the problem. 8) Suppose that the value V of a certain product decreases, or depreciates, with time t, in months, where V(t) = 7-16t. (t + ) Find V(t). t A) 16 B) 1 C) 7 D)

16 9) Suppose that the value V of a certain product decreases, or depreciates, with time t, in months, where V(t) = 100-0t. (t + ) Find V(t). t A) 80 B) 0 C) 100 D) 60 0) Suppose that the cost C of removing p% of the pollutants from a chemical dumping site is given by C(p) = $0, p Can a company afford to remove 100% of the pollutants? Explain. A) Yes, the cost of removing p% of the pollutants is $0,000, which is certainly affordable. B) No, the cost of removing p% of the pollutants is $00, which is a prohibitive amount of money. C) Yes, the cost of removing p% of the pollutants is $00, which is certainly affordable. D) No, the cost of removing p% of the pollutants increases without bound as p approaches 100. Sketch a possible graph of a function that satisfies the given conditions. 1) f(0) = and x 0 f(x) = 6 y x - - A) -6 6 y x

17 B) 6 y x C) 6 y x D) 6 y x

18 ) f(-1) = -7 ; f(x) = -; x (-1) - x (-1) + f(x) = -7 y - - x A) -10 y - - x B) -10 y - - x

19 C) y - - x D) -10 y - - x The graph of y = f(x) is shown. Use the graph to answer the question. ) Is f continuous at x = -1.5? 5 1 y x A) No B) Yes

20 ) Is f continuous at x = 0? x A) No B) Yes y 5) Is f continuous at x = 0? 5 y x -1 A) No B) Yes Provide an appropriate response. x 6) Determine where the function H(x) = + 7 is continuous. x + x - 6 A) (-, -) (-, ) (, ) B) (-, ) (, ) C) (-, -) D) (-, -) (-, )

21 5x 7) Determine where the function f(x) = is continuous. x - A), B) (-, ) C) -, D) -,, 8) Determine the points at which the function is discontinuous. h(x) = A) 1 B) -1, 1 C) -1, 0, 1 D) None x - for x < -1 0 for -1 x 1 x + for x > 1 9) Use a graphing utility to approximate the partition numbers of the function to four decimal places: f(x) = x - 8x - x + 1. A) (-, -.976) B) (-, -.976) (0.18,.07) C) (-, -.976) (-.976, -0.70) D) (-, -.976) (-.976, -0.70) (-0.70, 0.18 ) (0.18,.07) 50) Use a graphing utility to find the discontinuities of the given rational function. x + 1 g(x) = x + x + 10x - 1 A) B) 1 C) -1 D) Continuous at all values of x 51) Use a graphing utility to find the discontinuities of the given rational function. x + 1 g(x) = x + x + 10x - 1 A) B) -1 C) 1 D) Continuous at all values of x

22 5) Use a graphing utility to find the discontinuities of the given rational function. x f(x) = + x + 1 x + x + 5x - 8 A) B) -1 C) 1 D) Continuous at all values of x 5) Solve the inequality and express the answer in interval notation: A) (-5, 0) B) (-5, 0) (, ) C) (-5, ) D) (, ) x - x > 0. x + 5 5) Use a sign chart to solve the inequality. Express answers in interval notation. x > 16 A) (-, ) B) (-, ) C) (, ) D) (-, -) (, ) 55) Use a sign chart to solve the inequality. Express answers in interval notation. x + 6 < x A) {} B) C) (, ) D) (-, -) 56) Use a sign chart to solve the inequality. Express answers in interval notation. - 5 > 0 -x - A) -, B) (0, ) C) -, - D) -,

23 Solve the problem. 57) The cost of renting a snowblower is $0 for the first hour (or any fraction thereof) and $5 for each additional hour (or fraction thereof) up to a maximum rental time of 5 hours. Write a piecewise definition of the cost C(x) of renting a snowblower for x hours. Is C(x) continuous at x =.5? 0 if 0 x 1 5 if 1 x A) C(x) = 0 if x ; No 5 if x 0 if x 5 0 if 0 < x 1 5 if 1 < x B) C(x) = 0 if < x ; Yes 5 if < x 0 if < x 5 C) C(x) = D) C(x) = 0 if 0 < x 1 5 if 1 < x 0 if < x ; No 5 if < x 0 if < x 5 5 if 0 < x 1 0 if 1 < x 5 if < x ; No 0 if < x 5 if < x 5 Find average rate of change for the function over the given interval. 58) y = x + 6x between x = 5 and x = 9 A) 15 B) 80 9 C) 15 D) 0 59) y = 7x + 7x + between x = -6 and x = -1 A) 5 B) 5 C) - D) - 160

24 60) Find the average rate of change for f(x) = x if x changes from to 8. A) 7 B) C) 1 D) ) Find the average rate of change of y with respect to x if x changes from to 5 in the function y = x + x. A) 9 B) 11 C) D) Find the instantaneous rate of change for the function at the value given. 6) Find the instantaneous rate of change for the function x + x at x = 6. A) 16 B) 10 C) 1 D) 60 6) Find the instantaneous rate of change for the function f(x) = 5x + x at x = -. A) -1 B) -9 C) -1 D) 6 Provide an appropriate response. 6) Use the four step process to find f'(x) for the function f(x) = 5x - x. A) 10x - B) 5h - C) 5h - h D) 10x + 5h -

25 65) Use the four step process to find f'(x) for the function f(x) = A) B) C) - D) - (h + x) x (x + h) (h + x) x (x + h) (h + x) x (x + h) (h + x + xh) x (x + h) x. 66) Use the four step process to find f'(x) for the function f(x) = A) B) - C) D) - 6 (x - 6)(x + h - 6) x (x - 6)(x + h - 6) 1 (x - 6)(x + h - 6) 6 h(x - 6)(x + h - 6) x. 6 - x Use the definition f'(x) = f(x + h) - f(x) to find the derivative at x. h 0 h 67) f(x) = 9x - 16 A) -9 B) 9 C) 9x D) -7 68) f(x) = 10-1x A) -8x B) -8x C) 10-8x D) 10-1x 69) f(x) = x + 9x A) x + 7x B) x + 7x C) + 7x D) + 9x

26 Provide an appropriate response. 70) Find the slope of the secant line joining (, f()) and (, f()) for f(x) = -x - 8. A) -55 B) 55 C) 15 D) ) Find the slope of the graph f(x) = -x + x at the point (1, ). A) 1 B) -1 C) D) - 7) Find the slope of the line tangent to the graph of the function at the given value of x. y = x + x + x + at x = - A) -5 B) 65 C) 67 D) -50 7) Given f(x + h) - f(x) = xh + h + h, find the slope of the tangent line at x =. A) 0 B) C) 8 D) 16 Find the equation of the tangent line to the curve when x has the given value. 7) f(x) = -- x ; x = A) y = -x B) y = 8x - 1 C) y = -8x + 1 D) y = x ) Find the equation of the tangent line to the graph of the function at the given value of x. f(x) = x + 5x at x = A) y = 1x - 16 B) y = - 5 x C) y = 1 x D) y = - 9x - 80

27 Solve the problem. 76) Suppose an object moves along the y-axis so that its location is y = f(x) = x + x at time x (y is in meters and x is in seconds). Find the average velocity (the average rate of change of y with respect to x) for x changing from to 9 seconds. A) 8 m/s B) 15 m/s C) m/s D) 1 m/s 77) Suppose an object moves along the y-axis so that its location is y = f(x) = x + x at time x (y is in meters and x is in seconds). Find the average velocity for x changing from to + h seconds. A) 1 - h m/s B) 1 + h m/s C) 7 - h m/s D) 7 + h m/s 78) Suppose an object moves along the y-axis so that its location is y = f(x) = x + x at time x (y is in meters and x is in seconds). Find the instantaneous velocity at x = seconds. A) 8 m/s B) 10 m/s C) 9 m/s D) 0 m/s List the x-values in the graph at which the function is not differentiable. 79) A) x = 1 B) x = -1 C) x = 0 D) x =

28 80) A) x = -, x = 0, x = B) x = -, x = C) x = -, x = D) x = -, x = 0, x = 81) A) x = -, x = 0, x = B) x = C) x = 0 D) x = -, x = Solve the problem. 8) If an object moves along a line so that it is at y = f(x) = x - 7x - 6 at time x (in seconds), find the instantaneous velocity function v = f'(x). A) x - 7 B) x - 7 C) x - 7 D) x - 7 8) If an object moves along a line so that it is at y = f(x) = 8x at time x (in seconds), find the velocity at x = 1 (y is measured in feet). A) 8 ft / s B) 160 ft/s C) 6 ft/sec D) 16 ft / s

29 8) The electric power p (in W) as a function of the current i (in A) in a certain circuit is given by p(i) = 10i + 6i. Find the instantaneous rate of change of p with respect to i for i = 0.9 A. A) 7 W/A B) 81 W/A C) 7.7 W/A D) 6.8 W/A Provide an appropriate response. 85) Find f'(x) if f(x) = π. A) f'(x) = π B) f'(x) = 0 C) f'(x) = 1 D) f'(x) = π 86) Find y' if y = 5. 8 A) 1 B) 5 x 8 C) 0 D) ) Find y' if y = 6x. A) x B) 6 C) 0 D) x 88) Find f'(x) for f(x) = x 5 + 6x 8. A) x + 6x 7 B) 10x 6 + 8x 9 C) 10x + 8x 7 D) 10x + 8x 89) Find the derivative of y = x5-7x -. x A) y = 9x + 8x - B) y = 18x + 8x - C) y = 9x - + 8x - D) y = 9x + 8x

30 90) Let f and g be functions that satisfy f'() = and g'() = -. Find h'() for h(x) = f(x) - g(x) +. A) 9 B) 11 C) 5 D) 91) Find f'(x) if f(x) = x + 6x 7. A) 1x + x 6 B) x + 7x 6 C) 7x + 1x 6 D) x 5 + 7x 8 9) Find f'(x) if f(x) = 6x - + 8x + 11x. A) f(x) = -1x -1 + x B) f'(x) = -1x -1 + x + 11 C) f'(x) = -1x - + x D) f'(x) = -1x - + x ) Find f'(x) if f(x) = 9x 7/5-5x A) f'(x) = 6 x /5-10x 5 B) f'(x) = 6 x 6/5-10x 5 C) f'(x) = 6 x 6/5-10x D) f'(x) = 6 x /5-10x ) Find: d dx 5 - x x A) x x 5 B) 16-0 x x C) x x D) 1 - x x 5

31 95) Find: dy if y = t - - 5t -1 dt A) t 5 t B) -1t -5-5t - C) -1 t 5-5t D) -1t t - 96) Find: d - 5 x dx x A) 1-5 x -/ x B) 1 x -5-15x / C) x -/ x D) -16x -5-5 x -/ 97) Find d (6v v 5.8 ) dv A).v v.8 B).v v.7 C).v v -.7 D).v v ) Find dy for y = 1 + x7. dx x 10 A) -x x x B) 6 9x x C) 6 + 9x 10 D) -x x 6 10

32 99) Find the equation of the tangent line at x = 7 for f(x) = 6 - x. Write the answer in the form y = mx + b. A) y = - 1x + 55 B) y = - x C) y = 7x + 55 D) y = 1x ) Find the equation of the tangent line at x = - 6 for f(x) = x. Write the answer in the form y = mx + b. A) y = 16x + 18 B) y = 5x + 16 C) y = 18x + 16 D) y = 16x ) Find the values of x where the tangent line is horizontal for f(x) = x - x - 9. A) x = 0, x = - 9 B) x = 0, x = 9 C) x = 0, x = - D) x = 0, x = 10) Find the equation of the tangent line at x = for f(x) = + x - x - x. Write the answer in the form y = mx + b. A) y = -9x + 5 B) y = -x + 60 C) y = -7x + 68 D) y = -x + 8 Solve the problem. 10) An object moves along the y-axis (marked in feet) so that its position at time t (in seconds) is given by f(t) = 9t - 9t + t + 7. Find the velocity at three seconds. A) 19 feet per second B) 197 feet per second C) 190 feet per second D) 109 feet per second

33 10) A pen manufacturer determined that the total cost in dollars of producing x dozen pens in one day is given by: C(x) = 50 + x x, 0 x 100 Find the marginal cost at a production level of 70 dozen pens and interpret the result. A) The marginal cost is $0.58/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $0.58. B) The marginal cost is $0.60/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $0.60. C) The marginal cost is $0.6/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $0.6. D) The marginal cost is $0.59/doz. The cost of producing 1 dozen more pens at a production level of 70 dozen pens is approximately $ ) According to one theory of learning, the number of items, w(t), that a person can learn after t hours of instruction is given by: w(t) = 15 t, 0 t 6 Find the rate of learning at the end of eight hours of instruction. A) 5 items per hour B) 5 items per hour C) 0 items per hour D) 60 items per hour Find y for the given values of x 1 and x. Find dy. 106) y = x + ; x = 18, Δx = 0.5 A) 5 B) 0.1 C) 0.5 D) 1 107) y = 5x - 7x - 7 A) 10x - 7 dx B) 10x dx C) 10x - 1 dx D) (10x - 7) dx

34 108) y = x 5x x - A) dx 5x + 1 B) 15x - dx 5x + 1 C) 15x + dx 5x + 1 D) 15x + dx 5x + 1 Provide an appropriate response. 109) Evaluate dy and y for y = f(x) = x -7x + 5, x = 7, and dx = x = 0.5. A) dy =.5; y =.75 B) dy =.5; y =.5 C) dy =.75; y =.75 D) dy =.75; y =.5 110) Evaluate dy and y for y = f(x) = x - x, x =, and dx = x = 0.. A) dy = 15.18; y = 1. B) dy = 1.; y = C) dy = 1.; y = 1. D) dy = 15.18; y = ) A spherical balloon is being inflated. Find the approximate change in volume if the radius increases from 6. cm to 6. cm. (Recall that V = πr.) A) 0.99π cm B) 15.76π cm C) cm D) 0.75π cm Solve the problem. 11) A cube inches on an edge is given a protective coating 0.1 inches thick. About how much coating should a production manager order for 900 cubes? A) About 0 in. B) About 5760 in. C) About 10 in. D) About 860 in.

35 11) One hour after x milligrams of a particular drug are given to a person, the change in body temperature T (in degrees Fahrenheit) is given by T = x 1 - x 9, where 0 x. Approximate the changes in body temperature produced by changing the drug dosage from 1 to 1.9 milligrams. Round to the nearest hundredth when necessary. A) 0. F B) 1.5 F C) 1.67 F D).17 F 11) V = πr, where r is the radius, in centimeters. By approximately how much does the volume of a sphere increase when the radius is increased from 1.0 cm to 1.1 cm? (Use.1 for π.) A) 1.1 cm B) 1. cm C) 1.5 cm D) 0.1 cm Provide an appropriate response. 115) Suppose that the total profit in hundreds of dollars from selling x items is given by P(x) =x - 5x Find the marginal profit at x = 5. A) $ B) $15 C) $5 D) $5 116) The revenue (in thousands of dollars) from producing x units of an item is modeled by R(x) = 5x x. Find the marginal revenue at x = A) $.50 B) $10.00 C) $10,00.00 D) $.00

36 117) Let C(x) be the cost function and R(x) the revenue function. Compute the marginal cost, marginal revenue, and the marginal profit functions. C(x) = 0.000x x + 00x + 0,000 R(x) = 50x A) C'(x) = 0.001x x + 00 R'(x) = 50 P'(x) = x x + 50 B) C'(x) = 0.001x x + 00 R'(x) = 50 P'(x) = 0.001x x - 50 C) C'(x) = 0.001x x + 00 R'(x) = 50 P'(x) = 0.001x x ) The total cost to produce x units of paint is C(x) = (5x + )(7x + ). Find the marginal average cost function. A) C'(x) = 70x + 1 B) C'(x) = 5x C) C'(x) = 70-1 x D) C'(x) = 5-1 x x 119) The total profit from selling x units of doorknobs is P(x) =(6x - 7)(9x - 8). Find the marginal average profit function. A) P'(x) = 5-56 x B) P'(x) = 5x -111 C) P'(x) = 5x - 56 D) P'(x) = x 10) The total cost in dollars of producing x lawn mowers is given by C(x) =, x - x. Find the marginal average cost at x = 0, C'(0) and interpret the result. A) -$1.; a unit increase in production will decrease the average cost per unit by approximately $1. at a production level of 0 units. B) -$10.; a unit increase in production will decrease the average cost per unit by approximately $10. at a production level of 0 units. C) -$0.; a unit increase in production will decrease the average cost per unit by approximately $0. at a production level of 0 units. D) -$1.; a unit increase in production will decrease the average cost per unit by approximately $1. at a production level of 0 units.

37 Solve the problem. 11) The demand equation for a certain item is p = 1 - x and the cost equation is C(x) = 7,000 + x. Find the marginal profit at a production level of,000 and interpret the result. A) $1; at the,000 level of production, profit will increase by approximately $1 for each unit increase in p r o d u c t i o n. B) $16; at the,000 level of production, profit will increase by approximately $16 for each unit increase in p r o d u c t i o n. C) $7; at the,000 level of production, profit will increase by approximately $7 for each unit increase in p r o d u c t i o n. D) $; at the,000 level of production, profit will increase by approximately $ for each unit increase in p r o d u c t 1, 0 0 0

38 i o n. 1) A company is planning to manufacture a new blender. After conducting extensive market surveys, the research department estimates a weekly demand of 600 blenders at a price of $50 per blender and a weekly demand of 800 blenders at a price of $0 per blender. Assuming the demand equation is linear, use the research department's estimates to find the revenue equation in terms of the demand x. A) R(x) = 80x - 0x B) R(x) = 80x - x 0 C) R(x) = 0x + x 0 D) R(x) = 80x - 0 1) Suppose the demand for a certain item is given by D(p) = -p + p + 8, where p represents the price of the item. Find D'(p), the rate of change of demand with respect to price. A) D'(p) = -p + B) D'(p) = -6p + C) D'(p) = -p + D) D'(p) = -6p + Calculus for Business Economics Life Sciences and Social Sciences 1th Edition Barnett TEST BANK Full download at: Calculus for Business Economics Life Sciences and Social Sciences 1th Edition Barnett SOLUTIONS MANUAL Full download at: calculus for business economics life sciences and social sciences 1th edition pdf calculus for business 1th edition pdf calculus for business barnett 1th edition calculus for business economics life sciences and social sciences 11th edition calculus for business economics life sciences 1th edition pdf calculus for business economics life sciences answers calculus for business economics life sciences and social sciences 15th edition isbn

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