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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
(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 t 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
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
(c) Find the x-coordinate of each point on the curve where the tangent line is vertical. 6. Consider the differential equation dy
= 2y .
e (a) Find a solution y = f ( x ) to the differential equation satisfying f ( 0) = 1 .
(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.
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- Fall '14