4-ĥ dy x Consider the differential equation =. (d) Write expressions for the squirrel s acceleration at (), velocity vt (), and distance xt () from building A that are valid for the time interval 7 < t < 10.
(b) At what time in the interval 0 t 18 is the squirrel farthest from building A? How far from building A is the squirrel at that time? (c) Find the total distance the squirrel travels during the time interval 0 t 18. (a) At what times in the interval 0 < t < 18, if any, does the squirrel change direction? Give a reason for your answer. For 0 t 18, the squirrel s velocity is modeled by the piecewise-linear function defined by the graph above. A squirrel starts at building A at time t = 0 and travels along a straight, horizontal wire connected to building B. END OF PART A OF SECTION II -3-Ĥ CALCULUS AB SECTION II, Part B Time 45 minutes Number of problems 3 No calculator is allowed for these problems. How fast is the water level in the pool rising at t = 8 hours? Indicate units of measure in both answers. (d) Find the rate at which the volume of water in the pool is increasing at time t = 8 hours. Round your answer to the nearest cubic foot. (c) Use the results from parts (a) and (b) to approximate the volume of water in the pool at time t = 12 hours. (b) Calculate the total amount of water that leaked out of the pool during the time interval 0 t 12 hours. Show the computations that lead to your answer. V = pr h ) (a) Use a midpoint Riemann sum with three subintervals of equal length to approximate the total amount of water that was pumped into the pool during the time interval 0 t 12 hours. (Note: The volume V of a cylinder with radius r and height h is given by 2. During the same time interval, water is leaking from the pool at the rate R() t cubic feet -0.05t per hour, where Rt () = 25 e. The table above gives values of P() t for selected values of t. During the time interval 0 t 12 hours, water is pumped into the pool at the rate P() t cubic feet per hour. The pool contains 1000 cubic feet of water at time t = 0. (d) Does the line tangent to the graph of g at x = 0.3 lie above or below the graph of g for 0.3 < x < 1? Why? t P(t) The figure above shows an aboveground swimming pool in the shape of a cylinder with a radius of 12 feet and a height of 4 feet. (c) Write an equation for the line tangent to the graph of g at x = 0.3. (b) On what subintervals of ( 0.12, 1 ), if any, is the graph of g concave down? Justify your answer. x x (a) Find all values of x in the interval 0.12 x 1 at which the graph of g has a horizontal tangent line. The function g is defined for x > 0 with () 1 = 2, 1 g g ( x) = ( x + ) sin, x Ê and ( ) 1 ˆ = Á - 2 ( + 1 Ë ) g x x 1 cos. For this solid, each cross section perpendicular to the x-axis is a square.
y 4ln 3 x, the (c) The region R is the base of a solid. (b) Find the volume of the solid generated when R is revolved about the horizontal line y = 8. In the figure above, R is the shaded region in the first quadrant bounded by the graph of = ( - ) horizontal line y = 6, and the vertical line x = 2. Permission to use copyrighted College Board materials may be requested online at: AP Central is the official online home for the AP Program: .Ģ CALCULUS AB SECTION II, Part A Time 45 minutes Number of problems 3 A graphing calculator is required for some problems or parts of problems.
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