1. If f is the function given by f (x) = - + 5x - 1, then f'(2) = X (A) 4 (B) 6 (C) 7 (D) 11 2 . [be 3x dx = (A) 203* + C (B) 6ex + C (C) 18ex + C 63x+1 (D) + C 3x + 14. lff'(x) = 3x2+ 2x and f(2) = 3, then f(1)= (A) 10 (B) 7 (C) 10 (D) 13 t (minutes) 0 5 10 15 RU) 5. During an evacuation drill, people leave a building at a rate of R(t) people per minute, where t is the number of minutes since the start of the drill. Selected values of R(t) are shown in the table above. Using a right Riemann sum with three subintervals and data from the table, what is the approximation of the number of people who leave the building during the rst 15 minutes of the evacuation drill? (A) 230 (B) 1150 (C) 1375 (D) 2075 6. If y = x2 (ex - 1), then dy dx = (A) 2xe* (B) 2xe - 2x (C) xe*+ 2xe* - 2x (D) xe* + 2xet - x2 - 2x 7. A particle moves along the x-axis so that at any time t, t 2 0, its acceleration is a(t) = -4 sin(2t). If the velocity of the particle at t = 0 is v(0) = 7 and its position at t = 0 is x(0) = 0, then its position at time t is x(t) = (A) sin(2t) + 5t (B) sin(2t) + 7t (C) sin(2t) + 9t (D) 16 sin(2t) + 7ty l x 1 Graph of f \" 8. The graph of f \In(x + h) - In(x) 9. When x = 2e, lim is h-0 h (A) (B) 1 2e (C) In (2e) (D) nonexistent 10 . If dy = x* - 2x3+ 3x - 1, then evaluated at x = 2 is dx dx (A) 11 (B) 24 (C) 26 (D) 125.2 x for x 0 11. Let f be the function defined above. What is [ f ( x) dx ? (A) (B) W / N (C) (D) nonexistent aldy 12. Given that 3x - tan y = 4, what is in terms of y ? dx (A) dy = 3 sin y dx dy (B) = 3 cosy dx dy (C) = 3 cos ycot y dx dy 3 (D) = dx 1 + 9y 2dy 12. Given that 3x - tan y = 4, what is in terms of y ? dx (A) dy = 3 sin y dx dy (B) = 3 cosy dx dy (C) = 3 cos ycot y dx dy 3 (D) = dx 1 + 9y 213. For time t 2 1, the position of a particle moving along the x- axis is given by p(t) = J? 2. At what time t in the interval 1 S t S 16 is the instantaneous velocity of the particle equal to the average velocity of the particle over the interval 1 S t S 16 ? 121 25 (A) 1 (B) 25 (C) ? (D) 25 d 14. If f is a differentiable function and y = sin ( f (1:2)), what is E), when x = 3 ? (A) CDS(f'(9)) (B) 6cos(f(9)) (C) f'(9)008(f(9)) (D) 6f'(9)008(f(9)) 15. The graph of g', the first derivative of the function 3, consists of a semicircle of radius 2 and two line segments, as shown in the gure above. If 3(0) = 1, what is g(3] ? (A) 1r+l (B) n+2 (C) 21r+l (D) 2x+2 16. Let f be the function given by f (x) = x3 6x2 15x. What is the maximum value off on the interval [0, 6] ? (A) 0 (B) 5 (C) 6 (D) 8 1 17. dx = x- + 4x +5 (A) arctan (x + 2) + C (B) arcsin (x + 2) + C (C) In x2 + 4x + 5 + C 1 (D) + C 7* + 2x-+5x 18. Let f be the function defined by f(x) = /x. What is the approximation for f (10) found by using the line tangent to the graph of f at the point (8, 2) ? 25 (A) E (B) 12 (C) 13 6 (D) w /4x2 19. lim4is x)O (3'74in (A) 0 (E) g (C) 8 (D) nonexistent 20. Let g be a tvvice-rlifferentiable1 increasing function of I. If 3(0) = 20 and g(10) = 220, which of the following must be true on the interval 0 0 for all I in the interval