f x x, where f x (E) f, where ln

Transcription

1 AB Review 08 Calculator Permitted (unless stated otherwise) 1. h0 ln e h 1 lim is h (A) f e, where f ln (B) f e, where f (C) f 1, where ln (D) f 1, where f ln e ln 0 (E) f, where ln f f 1 1, where t is time in 6 4. The position of an object attached to a spring is given by y t cos5t sin 5t seconds. In the first 4 seconds, how many times is the velocity of the object equal to 0? (A) Zero (B) Three (C) Five (D) Si (E) Seven 3. Let f be the function given by f cos ln 3. What is the least value of at which the graph of f changes concavity? (A) 0.56 (B) 0.93 (C) 1.18 (D).38 (E) If 0 4, of the following, which is the greatest value of such that t t dt tdt? 0 (A) 1.35 (B) 1.38 (C) 1.41 (D) 1.48 (E) 1.59

2 5. Let f be a differentiable function such that f 3 15, f 6 3, f 3 8, and f 1 function g is differentiable and g f for all. What is the value of g 3? 1 (A) (E) The value of g3 1 (B) (C) 1 (D) cannot be determined from the information given 6. The 6. Let f be a continuous function on the closed interval 3,6. If f 3 1 and Intermediate Value Theorem guarantees that (A) f (B) f c for at least one c between 3 9 (C) 1 f 3 for all between 3 (D) f c 1 for at least one c between 3 (E) f c 0 for at least one c between 1 and 3 f 6 3, then the 7. The first derivative of the function f is defined by f sin 3 for 0. On what interval(s) is f increasing? (A) (B) (C) (D) and (E) 0 1 and 1.691

3 8. Let f be the function given by cos 1 f dt t for 1 t 3 1. At which of the following values of 1/3 does f attain a relative maimum? (A) and (B) 0.4 and (C) 0.4 only (D) (E) Let f be the function defined by f ln. What is the value of c for which the instantaneous rate of change of f at c is the same as the average rate of change of f over 1,4? (A) (B) 1.44 (C).164 (D).34 (E).45 3/ 10. The height, h, in meters, of an object at time t is given by ht 4t 4t 16t. What is the height of the object at the instant when it reaches its maimum upward velocity? (A).545 meters (B) meters (C) meters (D) meters (E) meters

4 11. (01, AB-5) (No Calculator) The rate at which a baby bird gains weight is proportional to the difference between its adult weight and its current weight. At time t 0, when the bird is first weighed, its weight is B t is the weight of the bird, in grams, at time t days after it is first weighed, then 0 grams. If Let y db B dt 5. B t be the solution to the differential equation above with the initial condition B 0 0. (a) Is the bird gaining weight faster when it weighs 40 grams or when it weighs 70 grams? Eplain your reasoning. d B (b) Find dt graph. in terms of B. Use d B dt to eplain why the graph of B cannot resemble the following (c) Use separation of variables to find initial condition B0 0. y B t, the particular solution to the differential equation with

5 1. (011, AB-1) (Calculator Permitted) For 0 t 6, a particle is moving along the -ais. The particle s position, t/4 t, is not eplicitly given. The velocity of the particle is given by vt e 1 t acceleration of the particle is given by /4 t a t e cose /4 sin 1. The 0. (a) Is the speed of the particle increasing or decreasing at time t 5.5? Give a reason for your answer. and (b) Find the average velocity of the particle for the time period 0 t 6. (c) Find the total distance traveled by the particle from time t 0 to t 6. (d) For 0 t 6, the particle changes direction eactly once. Find the position of the particle at that time.