Calculus Exam Answers Part B

CALCULUS BC SECTION I, Part II Tue-50 minutes Number of questions-17 A GRAPHING CALCULATOR IS REQUIRED FOR SOME QUESTIONS ON THIS PART OF THE EXAMINATION. Directions: Solve each of the following problems, using the available space for scratchwork. After examining the fona of the choices, decide which is the beat of the choices given and till in the corresponding oval on the answer sheet. No credit will be given for anything written in the test book. Do not spead too much time on any one problem. BE SURE YOU ARE USING PAGE 3 OF THE ANSWER SUKET TO RECORD YOUR ANSWERS TO QUESTIONS NUMBERED 76-92. YOU MAY NOT RETURN TO PAGE 2 OF THE ANSWER SHEET. In this test: (1) The exoct numerical value of the correct anawer does not always appear among the choices given. When this huppens, select from among the chofess the number that best approximates the cract numerical value. (2) Uitless otherwise specified, the domain of a function fis assumed to be the set of all real numbers for which f(x) is a real number. (3) The inverse of a trigonometric fanction / may be indicated using the inverss function setation f ^ - 1 or with the prefix "arc" (eg, sinarcsin x). E A Gruph of f 76. The graph of the function is shown above. Which of the following statements must be falte? (A) /(a) exists. (B) f(x) is defined for emptyset< x < a . (C)/is not continuous at x = a (D) lim x -> ∞ f(x) exists. (05) lim x -> ∞ f' * (x) raists 77. Let P(x) = 3x ^ 2 - 5x ^ 3 + 7x ^ 4 + 3x ^ 5 be the fifth-degree Taylor polynomial for the fonction x = 0 What f^ * (0) (A)-30 (8)-15 - 5/6 (0) - 1/6 (3) f ^ 1 = 6x - 15x ^ 2 + 28x ^ 3 15) f^ prime prime = 6 - 30x + 3.28x ^ 2 + 60y ^ 5 f^ prime prime prime = - 30 + 163x + 180x ^ 2 C D 78. The radius of a circle is increasing at a constant rate of 0.2 meters per second. What is the rate of increase in the Catea of the circle at the instant when the cucsinference of the circle is 20v moters? (A) 0.04 m²/sc (8) 4pi * m ^ 2 /sec de (C) t*pi * m ^ 2 /sec (D) 20pi * m ^ 2 /sec (E) 100pi * m ^ 2 / t * oc C = 2pi ) 20M = 2NY 10 = C (x) f(x) (x) g' * (x) -1 6 5 -2 1 3 -3 -1 2 3 1 -2 2 3 (B) 6 (9 79. The table above gives values of f * f^ * 8. and g" at selected values of x. IF then k'(1) - (A) 3 (D)) 10 (B) 12 h' * (x) = f' * (g(x)) * g' * (x) h' * (i) = f' * (0(1)) * g' * (i) = f' * (- 1) + 2 = 5(2) \\ =10 aligned A A 10. Insects destroyed a crop at the rate of (100e ^ - 0.1)/(2 - e ^ (-3r)) tons per day, where time t is the ssarett ton, how many toos did the insects destroy the time interval 7 <= t <=14 ? (C) 88 (D) 50 (A) 125 (B) 100 (B) 12 dt. 124.994 432 01 Creph off 81. The graph of the function / is shown in the figure above. The valve of lin sin(/(x)) is (A) 0.909 (B) 0.841 (C)0.141 (D) -0.416 (B) noncxistent (ddA)/(dt) = 2nr * d/dt (A) dc4 dCt = 21r(10) (.z) = 4pi int 7 ^ 14 100e^ -,it 3 - e ^ (-3t) wt = 13y ^ 2 lim x -> 1 sin(f(i)) lim x -> 1 sin(2) approx,90929 dx = h(x) = f(g(x))