SHOW WORK! Chapter4Questions. NAME ID: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
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1 NAME ID: Date: Chapter4Questions Multiple Choice Identify the choice that best completes the statement or answers the question. SHOW WORK! 1. Find the indefinite integral 1u 4u du. a. 4u u C b. 1u 4u C c. 1u u C d. 4u 4u C e. 4u 4 C. Find the indefinite integral and check the result by differentiation. z 1z 9 z 4 dz a. z 1 z 9 z C b. z z z c. z z z C d. z z z e. z z z C. Solve the differential equation. dp dx 15x 4 5, P 8 4. An evergreen nursery usually sells a certain shrub after 4 years of growth and shaping. The growth rate during those 4 years is approximated by dh.5t, where t is the time in years and h is dt the height in centimeters. The seedlings are 15 centimeters tall when planted (t ). Find the height after t years. a. h(t) 1.5t 1t b. h(t) 1.5t t 15 c. h(t) 1.5t 15 d. h(t).5t t 15 e. h(t).5t 1 5. The height above the ground of an object thrown upward from a point s feet above the ground with an initial velocity of v feet per second is given by the function f(t) 1t v t s. A balloon, rising vertically with a velocity of 4 feet per second, releases a sandbag at the instant it is feet above the ground. At what velocity will it hit the ground? Round your answer to three decimal places. a..111 ft/sec b ft/sec c ft/sec d ft/sec e..81 ft/sec a. Px x 5 5x b. Px x 5 94 c. Px x 5 5x 94 d. Px x 5x 94 e. Px x 5 C 1
2 . The maker of an automobile advertises that it takes 1 seconds to accelerate from 5 kilometers per hour to 5 kilometers per hour. Assuming constant acceleration, compute the distance, in meters, the car travels during the 1 seconds. Round your answer to two decimal places. a..9 m b m c m d. 4. m e. 9.8 m. Use the properties of summation and Theorem 4. to evaluate the sum. 4 i 1 4i 8 a. 115 b. 119 c. 18 d. 44 e. 8. Use the properties of summation and Theorem 4. to evaluate the sum. i 1 i i 8 a.,15 b. 4, c. 8,5 d. 58, e., 9. Evaluate the following definite integral by the limit definition. 4 9s 4 ds a. 1 b. 4 c. 4 d. 19 e Write the limit lim x n i 1 4c i c i x i, as a definite integral on the interval,8 where c i is any point in the i th subinterval. a. 4x x 8 dx b. 4x x 8 dx 8 c. 4c i c i x i 8 d. 4x x dx c i e. 4c i c i x i
3 11. The graph of the function g y y is given below. Which of the following definite integrals yields the area of the shaded region? 1. Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral. 4 1 s d s a. b. 15 c. 4 d. 4 e Evaluate the integral. a. y dy b. y dy 8 c. y dy d. y dx e. y dy 4x dx given, x dx x dx x dx dx 1. a. 15 b , 1, 1, c. 1,1 d. 4 e.,
4 14. Evaluate the definite integral of the algebraic function. 5u 4du Use a graphing utility to verify your results. a b. 1 c. 9.5 d. 159 e Evaluate the definite integral of the function. 5x t 5cos tdt Use a graphing utility to verify your results. a. 5 b. 5 1 c. 5 d. 5 1 e Find the area of the region bounded by the graphs of the equations y x x, x 4, y. Round your answer to the nearest whole number. a. 8 b. 9 c. 49 d. e Find the average value of fx interval 1,. a. 4 b. 5 c. 5 d. 8 5 x 5 on the x e The volume V in liters of air in the lungs during a five-second respiratory cycle is approximated by the model V.14t.15t.t where t is the time in seconds. Approximate the average volume of air in the lungs during one cycle. Round your answer to four decimal places. a. 1.8 liter b..94 liter c..44 liter d liter e..5 liter 19. Find F(x) given x Fx 1t 1dt. x a. F(x) 1 1t b. F(x) 1 1x c. F(x) d. F(x) 48 x e. F(x) 48 t 4
5 . Find F(x) given Fx x t 5 dt. x a. F(x) 9x 5 b. F(x) c. F(x) 1458x 5 d. F(x) 48x 5 e. F(x) 5
6 Chapter4Questions Answer Section MULTIPLE CHOICE 1. ANS: A PTS: 1 DIF: Easy REF: OBJ: Evaluate the indefinite integral of a function MSC: Skill NOT: Section 4.1. ANS: E PTS: 1 DIF: Medium REF: OBJ: Evaluate the indefinite integral of a function MSC: Skill NOT: Section 4.1. ANS: C PTS: 1 DIF: Medium REF: OBJ: Solve a differential equation MSC: Skill NOT: Section ANS: B PTS: 1 DIF: Easy REF: 4.1.5a OBJ: Solve a differential equation in applications MSC: Application NOT: Section ANS: B PTS: 1 DIF: Medium REF: 4.1.4b OBJ: Solve differential equations related to position/velocity/acceleration MSC: Application NOT: Section 4.1. ANS: C PTS: 1 DIF: Medium REF: b OBJ: Solve differential equations related to position/velocity/acceleration MSC: Application NOT: Section 4.1. ANS: C PTS: 1 DIF: Medium REF: OBJ: Evaluate a sum using summation properties MSC: Skill NOT: Section ANS: E PTS: 1 DIF: Medium REF: 4.. OBJ: Evaluate a sum using summation properties MSC: Skill NOT: Section ANS: B PTS: 1 DIF: Easy REF: 4..8 OBJ: Evaluate a definite integral by the limit definition MSC: Skill NOT: Section ANS: D PTS: 1 DIF: Easy REF: 4..1 OBJ: Write a limit as a definite integral on an interval MSC: Skill NOT: Section ANS: E PTS: 1 DIF: Medium REF: 4..1 OBJ: Write a definite integral for a bounded region MSC: Skill NOT: Section ANS: B PTS: 1 DIF: Easy REF: 4..5 OBJ: Evaluate a definite integral geometrically MSC: Skill NOT: Section ANS: B PTS: 1 DIF: Easy REF: 4.. OBJ: Evaluate the definite integral of a function MSC: Skill NOT: Section ANS: C PTS: 1 DIF: Medium REF: 4.4. OBJ: Evaluate the definite integral of a function MSC: Skill 1
7 15. ANS: C PTS: 1 DIF: Easy REF: OBJ: Evaluate the definite integral of a function MSC: Skill 1. ANS: D PTS: 1 DIF: Medium REF: OBJ: Calculate the area bounded by a function MSC: Application 1. ANS: A PTS: 1 DIF: Easy REF: 4.4.5a OBJ: Calculate the average value of a function over a given interval MSC: Skill 18. ANS: E PTS: 1 DIF: Medium REF: 4.4. OBJ: Calculate the average value of a function in applications MSC: Application 19. ANS: C PTS: 1 DIF: Medium REF: OBJ: Calculate the derivative of an integral using the Second Fundamental Theorem of Calculus MSC: Skill. ANS: B PTS: 1 DIF: Medium REF: OBJ: Calculate the derivative of an integral using the Second Fundamental Theorem of Calculus MSC: Skill
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