76. A particle moves along a straight line so that at time t > 0 the position of the particle is given by s(t), the velocity is given by v(t), and the acceleration is given by 0(3). Which of the following expressions gives the average velocity of the particle on the interval [2, 8] ? 8 (A) 52 0(3) d: (B) 5284:) d: (C) 3(8);s(2) (D) v(8) g v(2) (E) 12(8) v(2) x2+l (A) 0.281 (B) 0.102 (C) 0.102 (D) 0.260 (E) 0.282 2 77. If sin[ ) is an antiderivative for f(.x), then L f(x)dx = 79. A vase has the shape obtained by revolving the curve y = 2 + sin): from x = 0 to x = 5 about the xaxis, where x and y are measured in inches. What is the volume, in cubic inches, of the vase? (A) 10.716 (B) 25.501 (C) 33.666 (D) $1.113 (E) 80.115 80. The table above gives selected values of a function f. The function is twice differentiable with f \"(x) > 0. Which of the following could be the value of f '(3) ? (A) 0.6 (B) 0.7 (C) 0.9 (D) 1.2 (E) 1.5 81. At time t = 0 years, a forest preserve has a population of 1500 deer. If the rate of growth of the population is modeled by R(t) = 2000e .2 deer per year, what is the population at time t = 3 ? (A) 3987 (B) 5487 (C) 8641 (D) 10,141 (E) 12,62883. Let f and g be continuous functions such that f(x) dx = 9, , f(x) dx = 5, and |g(x) dx = -7. What is the value of | Cf(x) - 38(x)) dx ? (A) -23 (B) -19 (C) - 2 (D) 19 (E) 2384. The regions A, B, and C in the gure above are bounded by the graph of the function f and the x-axis. The area of region A is 14, the area of region B is 16, and the area of region C is 50. What is the average value off on the interval [0, 8] '3 (A) 6 (B) 10 (C) % (D) ? (E) 48 91 2 . What is the total t +1 85. A particle moves along the xaxis so that its velocity at time t 2 0 is given by v(t) : distance traveled by the particle from t = 0 to t = 2 ? (A) 0.214 (B) 0.320 (C) 0.600 (D) 0.927 (E) 1.600 86. Line 6 is tangent to the graph of y = e\"r at the point (k, 6\"). What is the positive value of k for which the yintercept of 6' is %? (A) 0.405 (B) 0.768 (C) 1.500 (D) 1.560 (E) There is no such value of k. 87. A differentiable function f has the property that f'(x) S 3 for l S x S 8 and f(5) = 6. Which of the following could be true? I. f(2) = 0 II. f(6) = 2 III. f(?) = 13 (A) I only (B) II only (C) I and II only (D) l and III only (E) II and III only 92. The table above gives values of the differentiable functions f and g, and f ', the derivative of f, at selected values of x. If g(x) = f_1(x), what is the value of g'(4)'? (A) % (B (C) % (D i (E) % 89. What is the area ofthe region enclosed by the graphs of y = e" 2, y = sin x, and x = 0 ? (A) 0.239 (B) 0.506 (C) 0.745 (D) 2.340 (E) 3.472 90. A particle moves along a line so that its velocity is given by v(l') = t3 + 21:2 + 2: for l: 2 0. For what values of r is the speed of the particle increasing? (A) (0, 0.177) and (1.256, co) (B) (01256) only (C) (0, 2.057) only (D) (0177,1256) only (E) (0.177, 1.256) and (2.057, m) 89. What is the area ofthe region enclosed by the graphs of y = e" 2, y = sin x, and x = 0 ? (A) 0.239 (B) 0.506 (C) 0.745 (D) 2.340 (E) 3.472 90. A particle moves along a line so that its velocity is given by v(l') = t3 + 21:2 + 2: for l: 2 0. For what values of r is the speed of the particle increasing? (A) (0, 0.177) and (1.256, co) (B) (01256) only (C) (0, 2.057) only (D) (0177,1256) only (E) (0.177, 1.256) and (2.057, m)