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Test Bank for Calculus of a Single Variable, 10th Edition

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    Test Bank Calculus TENTH EDITION Ron Larson Bruce Edwards

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    iii Contents Chapter P: Preparation for Calculus 1 Chapter 1: Limits and Their Properties 43 Chapter 2: Differentiation 82 Chapter 3: Applications of Differentiation 141 Chapter 4: Integration 230 Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions 280 Chapter 6: Differential Equations 354 Chapter 7: Applications of Integration 390 Chapter 8: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals 448 Chapter 9: Infinite Series 506 Chapter 10: Conics, Parametric Equations, and Polar Coordinates 581 Chapter 11: Vectors and the Geometry of Space 646 Chapter 12: Vector-Valued Functions 703 Chapter 13: Functions of Several Variables 740 Chapter 14: Multiple Integration 819 Chapter 15: Vector Analysis 901 Chapter 16: Additional Topics in Differential Equations 970

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    P.1 Graphs and Models 1 P.1 Graphs and Models Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Which of the following is the correct graph of ? a. d. b. e. c.

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    2 Chapter P: Preparation for Calculus ____ 2. Which of the following is the correct graph of ? a. d. b. e. c.

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    P.1 Graphs and Models 3 ____ 3. Find all intercepts: a. x -intercepts: ( ,0), ( ,0); y -intercepts: (0, ), (0, 3) b. x -intercept: (12, 0); y -intercepts: (0, ), (0, 3) c. x -intercepts: (4, 0), (–3,0); y -intercept: (0, ) d. x -intercepts: ( , 0), ( ,0); y -intercepts: (0, –12), (0, 12) e. x -intercept: ( , 0); y -intercept: (0, –12) ____ 4. Find all intercepts: a. x -intercepts: (–5, 0), (–2, 0), (2, 0); y -intercepts: (0, 0), (0, 10) b. x -intercepts: (–5, 0), (2, 0); y -intercept: (0, 10) c. x -intercepts: (–5, 0), (2, 0); y -intercept: (0, –10) d. x -intercepts: (–5, 0), (–2, 0), (2, 0); y -intercept: (0, 10) e. x -intercepts: (–5, 0), (–2, 0), (2, 0); y -intercept: (0, –10) ____ 5. Test for symmetry with respect to each axis and to the origin. a. symmetric with respect to the origin b. symmetric with respect to the x -axis c. symmetric with respect to the y -axis d. no symmetry e. A, B, and C ____ 6. Test for symmetry with respect to each axis and to the origin. a. symmetric with respect to the origin b. symmetric with respect to the y -axis c. symmetric with respect to the x -axis d. both B and C e. no symmetry

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    4 Chapter P: Preparation for Calculus ____ 7. Sketch the graph of the equation: a. d. b. e. c.

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    P.1 Graphs and Models 5 ____ 8. Sketch the graph of the equation: a. d. b. e. none of the above c.

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    6 Chapter P: Preparation for Calculus ____ 9. Find the points of intersection of the graphs of the equations: a. b. c. d. e. ____ 10. The resistance y in ohms of 1000 feet of solid metal wire at can be approximated by the model where x is the diameter of the wire in mils (0.001 in). Use a graphing utility to graph the model a. d.

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    P.1 Graphs and Models 7 b. e. c. ____ 11. The resistance y in ohms of 1000 feet of solid metal wire at can be approximated by the model where x is the diameter of the wire in mils (0.001 in). If the diameter of the wire is doubled, the resistance is changed by approximately what factor? In determining your answer, you can ignore the constant –0.46. a. b. c. d. e.

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    8 Chapter P: Preparation for Calculus ____ 12. Test for symmetry with respect to each axis and to the origin. a. symmetric with respect to the origin b. symmetric with respect to the y -axis c. symmetric with respect to the x -axis d. both B and C e. no symmetry ____ 13. Test for symmetry with respect to each axis and to the origin. a. symmetric with respect to the origin b. symmetric with respect to the x -axis c. symmetric with respect to the y -axis d. no symmetry e. A, B, and C ____ 14. Find all intercepts: a. x -intercepts: (0,0), (5,0), (-5,0); y -intercept: (0, -25) b. x -intercepts: (0,0), (5,0); y -intercept: (0, 0) c. x -intercepts: (0,0), (5,0), (-5,0); y -intercept: (0, 0) d. x -intercepts: (0,0), (5,0); y -intercept: (0, 5) e. x -intercepts: (0,0), (5,0), (25,0); y -intercept: (0, 0)

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    P.1 Graphs and Models 9 ____ 15. Sketch the graph of the equation: a. 0.5 1 1.5 2 2.5 –0.5 –1 –1.5 –2 –2.5 x 0.5 1 1.5 2 2.5 –0.5 –1 –1.5 –2 –2.5 y d. 1 2 3 4 5 –1 –2 –3 –4 –5 x 1 2 3 4 5 –1 –2 –3 –4 –5 y b. 1 2 3 4 5 –1 –2 –3 –4 –5 x 1 2 3 4 5 –1 –2 –3 –4 –5 y e. none of the above c. 0.25 0.5 0.75 1 1.25 –0.25 –0.5 –0.75 –1 –1.25 x 0.25 0.5 0.75 1 1.25 –0.25 –0.5 –0.75 –1 –1.25 y

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    10 Chapter P: Preparation for Calculus P.1 Graphs and Models Answer Section MULTIPLE CHOICE 1. ANS: B PTS: 1 DIF: Easy REF: Section 0.1 OBJ: Identify the graph of a semicircle MSC: Skill 2. ANS: B PTS: 1 DIF: Easy REF: Section 0.1 OBJ: Identify the graph of a cubic equation MSC: Skill 3. ANS: C PTS: 1 DIF: Easy REF: Section 0.1 OBJ: Calculate the intercepts of an equation MSC: Skill 4. ANS: D PTS: 1 DIF: Easy REF: Section 0.1 OBJ: Calculate the intercepts of an equation MSC: Skill 5. ANS: E PTS: 1 DIF: Easy REF: Section 0.1 OBJ: Identify the type of symmetry of the graph of an equation MSC: Skill 6. ANS: A PTS: 1 DIF: Easy REF: Section 0.1 OBJ: Identify the type of symmetry of the graph of an equation MSC: Skill 7. ANS: B PTS: 1 DIF: Easy REF: Section 0.1 OBJ: Graph a quadratic equation in y MSC: Skill 8. ANS: D PTS: 1 DIF: Med REF: Section 0.1 OBJ: Graph an absolute value equation MSC: Skill 9. ANS: C PTS: 1 DIF: Med REF: Section 0.1 OBJ: Calculate the points of intersection of the graphs of equations MSC: Skill 10. ANS: B PTS: 1 DIF: Med REF: Section 0.1 OBJ: Plot a rational model using the capabilities of a graphing utility MSC: Application 11. ANS: E PTS: 1 DIF: Med REF: Section 0.1 OBJ: Interpret a rational model MSC: Application 12. ANS: B PTS: 1 DIF: Easy REF: Section 0.1 OBJ: Identify the type of symmetry of the graph of an equation MSC: Skill 13. ANS: B PTS: 1 DIF: Easy REF: Section 0.1 OBJ: Identify the type of symmetry of the graph of an equation MSC: Skill 14. ANS: C PTS: 1 DIF: Easy REF: Section 0.1 OBJ: Calculate the intercepts of an equation MSC: Skill 15. ANS: D PTS: 1 DIF: Easy REF: Section 0.1 OBJ: Graph an equation in y MSC: Skill

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    P.2 Linear Models and Rates of Change 11 P.2 Linear Models and Rates of Change Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Estimate the slope of the line from the graph. a. 3 b. c. d. e. 6 ____ 2. Sketch the line passing through the point (3, 4) with the slope . a. d.

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    12 Chapter P: Preparation for Calculus b. e. c. ____ 3. Find the slope of the line passing through the pair of points. a. b. c. d. 0 e.

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    P.2 Linear Models and Rates of Change 13 ____ 4. Find the slope of the line passing through the points and . a. 63 b. 21 c. 42 d. 21 e. 42 ____ 5. If a line has slope and passes through the point , through which of the following points does the line also pass? a. b. c. d. e. ____ 6. A moving conveyor is built to rise 5 meters for every 7 meters of horizontal change. Find the slope of the conveyor. a. 0 b. c. d. e. ____ 7. A moving conveyor is built to rise 1 meter for every 5 meters of horizontal change. Suppose the conveyor runs between two floors in a factory. Find the length of the conveyor if the vertical distance between floors is 10 meters. Round your answer to the nearest meter. a. 61 meters b. 39 meters c. 51 meters d. 50 meters e. 41 meters

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    14 Chapter P: Preparation for Calculus ____ 8. Find the slope of the line . a. b. c. d. e. ____ 9. Find the y -intercept of the line . a. b. c. d. e. ____ 10. Find an equation of the line that passes through the point and has the slope m that is undefined. a. b. c. d. e. ____ 11. Find an equation of the line that passes through the point and has the slope . a. – b. + c. + 162 d. e.

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    P.2 Linear Models and Rates of Change 15 ____ 12. Find an equation of the line that passes through the points and . a. b. c. d. e. ____ 13. Find an equation of the line that passes through the points and . a. b. c. d. e. ____ 14. Use the result, “the line with intercepts has the equation , , ”, to write an equation of the line with x -intercept: and y -intercept: . a. b. c. d. e.

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    16 Chapter P: Preparation for Calculus ____ 15. Sketch a graph of the equation . a. d. b. e. c.

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    P.2 Linear Models and Rates of Change 17 ____ 16. Write an equation of the line that passes through the given point and is perpendicular to the given line. a. b. c. d. e. ____ 17. Write an equation of the line that passes through the given point and is parallel to the given line. a. b. c. d. e. ____ 18. Write an equation of the line that passes through the point and is perpendicular to the line . a. b. c. d. e. ____ 19. Write an equation of the line that passes through the point and is parallel to the line . a. b. c. d. e.

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    18 Chapter P: Preparation for Calculus ____ 20. A real estate office handles an apartment complex with units. When the rent is per month, all units are occupied. However, when the rent is , the average number of occupied units drops to . Assume that the relationship between the monthly rent and the demand is linear. Write a linear equation giving the demand in terms of the rent . a. b. c. d. e. ____ 21. A real estate office handles an apartment complex with units. When the rent is per month, all units are occupied. However, when the rent is $ , the average number of occupied units drops to . Assume that the relationship between the monthly rent and the demand is linear. Predict the number of units occupied if the rent is raised to . a. 43 units b. 54 units c. 57 units d. 49 units e. 46 units ____ 22. Find the distance between the point and line using the formula, for the distance between the point and the line . a. b. c. d. e.

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    P.2 Linear Models and Rates of Change 19 ____ 23. Suppose that the dollar value of a product in is and the rate at which the value of the product is expected to increase per year during the next years is . Write a linear equation that gives the dollar value of the product in terms of the year . (Let represent .) Round the numerical values in your answer to one decimal place, where applicable. a. b. c. d. e. ____ 24. A company reimburses its sales representatives per day for lodging and meals plus ¢ per mile driven. Write a linear equation giving the daily cost to the company in terms of , the number of miles driven. Round the numerical values in your answer to two decimal places, where applicable. a. b. c. d. e. ____ 25. A company reimburses its sales representatives per day for lodging and meals plus ¢ per mile driven. How much does it cost the company if a sales representative drives miles on a given day? Round your answer to the nearest cent. a. 227.20 b. 216.70 c. 136.35 d. 161.35 e. 191.70

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    20 Chapter P: Preparation for Calculus P.2 Linear Models and Rates of Change Answer Section MULTIPLE CHOICE 1. ANS: E PTS: 1 DIF: Easy REF: Section 0.2 OBJ: Estimate the slope of a line from its graph MSC: Skill 2. ANS: D PTS: 1 DIF: Easy REF: Section 0.2 OBJ: Sketch the line passing through a point with specified slope MSC: Skill 3. ANS: B PTS: 1 DIF: Easy REF: Section 0.2 OBJ: Calculate the slope of a line passing through two points MSC: Skill 4. ANS: C PTS: 1 DIF: Med REF: Section 0.2 OBJ: Calculate the slope of a line passing through two points MSC: Skill 5. ANS: A PTS: 1 DIF: Med REF: Section 0.2 OBJ: Identify a point on a line with specified properties MSC: Skill 6. ANS: B PTS: 1 DIF: Easy REF: Section 0.2 MSC: Application 7. ANS: C PTS: 1 DIF: Med REF: Section 0.2 OBJ: Calculate slopes in applications MSC: Application 8. ANS: E PTS: 1 DIF: Med REF: Section 0.2 OBJ: Manipulate a linear equation to determine its slope MSC: Skill 9. ANS: A PTS: 1 DIF: Med REF: Section 0.2 OBJ: Manipulate a linear equation to determine its y-intercept MSC: Skill 10. ANS: B PTS: 1 DIF: Easy REF: Section 0.2 OBJ: Write an equation of a line given a point on the line and its slope MSC: Skill 11. ANS: B PTS: 1 DIF: Easy REF: Section 0.2 OBJ: Write an equation of a line given a point on the line and its slope MSC: Skill 12. ANS: D PTS: 1 DIF: Easy REF: Section 0.2 OBJ: Write an equation of a line given two points on the line MSC: Skill 13. ANS: E PTS: 1 DIF: Med REF: Section 0.2 OBJ: Write an equation of a line given two points on the line MSC: Skill 14. ANS: E PTS: 1 DIF: Easy REF: Section 0.2 OBJ: Write an equation of a line given its x- and y-intercepts MSC: Skill 15. ANS: B PTS: 1 DIF: Med REF: Section 0.2 OBJ: Sketch the graph of a linear equation MSC: Skill 16. ANS: C PTS: 1 DIF: Med REF: Section 0.2 OBJ: Write an equation of a line given a point on the line and a line to which it is parallel/perpendicular MSC: Skill 17. ANS: A PTS: 1 DIF: Med REF: Section 0.2 OBJ: Write an equation of a line given a point on the line and a line to which it is parallel/perpendicular MSC: Skill 18. ANS: A PTS: 1 DIF: Med REF: Section 0.2 OBJ: Write an equation of a line given a point on the line and a line to which it is perpendicular MSC: Skill 19. ANS: A PTS: 1 DIF: Easy REF: Section 0.2 OBJ: Write an equation of a line given a point on the line and a line to which it is parallel MSC: Skill

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    P.2 Linear Models and Rates of Change 21 20. ANS: D PTS: 1 DIF: Med REF: Section 0.2 OBJ: Write linear equations in applications MSC: Application 21. ANS: E PTS: 1 DIF: Easy REF: Section 0.2 OBJ: Evaluate linear equations in applications MSC: Application 22. ANS: C PTS: 1 DIF: Med REF: Section 0.2 OBJ: Calculate the distance between a point and a line MSC: Skill 23. ANS: D PTS: 1 DIF: Easy REF: Section 0.2 OBJ: Write linear equations in applications MSC: Application 24. ANS: B PTS: 1 DIF: Easy REF: Section 0.2 OBJ: Write linear equations in applications MSC: Application 25. ANS: B PTS: 1 DIF: Easy REF: Section 0.2 OBJ: Evaluate linear equations in applications MSC: Application

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    22 Chapter P: Preparation for Calculus P.3 Functions and Their Graphs Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Evaluate (if possible) the function at . Simplify the result. a. –7 b. 17 c. 3 d. 7 e. undefined ____ 2. Evaluate (if possible) the function at . Simplify the result. a. b. c. d. e. ____ 3. Evaluate (if possible) the function at . Simplify the result. a. b. c. d. e. none of the above ____ 4. Let . Then simplify the expression . a. b. c. d. e. undefined

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    P.3 Functions and Their Graphs 23 ____ 5. Let . Evaluate the expression and then simplify the result. a. b. c. d. e. undefined ____ 6. Find the domain and range of the function . a. domain: range: b. domain: range: c. domain: range: d. domain: range: e. domain: range: ____ 7. Find the domain and range of the function . a. domain: range: b. domain: range: c. domain: range: d. domain: range: e. none of the above

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    24 Chapter P: Preparation for Calculus ____ 8. Find the domain and range of the function . a. domain: range: b. domain: range: c. domain: range: d. domain: range: e. domain: range: ____ 9. Evaluate the function at . a. b. c. d. e. ____ 10. Determine the domain and range of the function . a. domain: range: b. domain: range: c. domain: range: d. domain: range: e. domain: range: ____ 11. Determine whether y is a function of x . a. no b. yes

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    P.3 Functions and Their Graphs 25 ____ 12. Determine whether y is a function of x . a. no b. yes ____ 13. Use the graph of given below to find the graph of the function . a. d.

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    26 Chapter P: Preparation for Calculus b. e. c. ____ 14. Use the graph of given below to find the graph of the function .

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    P.3 Functions and Their Graphs 27 a. d. b. e. c.

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    28 Chapter P: Preparation for Calculus ____ 15. Given and , evaluate . a. b. c. d. e. ____ 16. Determine whether the function is even, odd, or neither. a. odd b. even c. neither ____ 17. Determine whether the function is even, odd, or neither. a. even b. odd c. neither ____ 18. Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even. a. b. c. d. e.

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