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4 water is pumped into an underground tank at a

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Unformatted text preview: 5 minutes Number of problems — 3 No calculator is allowed for these problems. 4. Water is pumped into an underground tank at a constant rate of 8 gallons per minute. Water leaks out of the tank at the rate of t + 1 gallons per minute, for 0 ≤ t ≤ 120 minutes. At time t = 0, the tank contains 30 gallons of water. (a) How many gallons of water leak out of the tank from time t = 0 to t = 3 minutes? (b) How many gallons of water are in the tank at time t = 3 minutes? (c) Write an expression for A(t ), the total number of gallons of water in the tank at time t. (d) At what time t, for 0 ˆ t ˆ 120, is the amount of water in the tank a maximum? Justify your answer. 5. Consider the curve given by xy 2 - x 3 y = 6. (a) Show that dy 3x 2 y − y 2 = . dx 2 xy − x 3 (b) Find all points on the curve whose x-coordinate is 1, and write an equation for the tangent line at each of these points. (c) Find the x-coordinate of each point on the curve where the tangent line is vertical. 6. Consider the differential equation dy 3x 2 = 2y . dx e (a) Find a solution y = f ( x ) to the differential equation satisfying f ( 0) = 1 . 2 (b) Find the domain and range of the function f found in part (a). END OF EXAMINATION Copyright © 2000 College Entrance Examination Board and Educational Testing Service. All rights reserved. AP is a registered trademark of the College Entrance Examination Board. -5-...
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