227sampleExam2Problems - y(1 = 2 6 A potato comes out of an...

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Math 227 Sections 4 and 5 Sample problems for Exam 2 These problems represent the range of material you should be prepared to encounter on the exam. The actual exam will be shorter. 1. Evaluate Z 1 1 1 x 3 = 2 dx: Make sure to show all steps. 2. Let D xy plane bounded by the curves y = p x and y = 0 and x = 4 : Suppose D is revolved around the y axis. (a) Sketch the solid region swept out. (b) Set up the volume integral using the disk/washer method. (c) Set up the volume integral using the shell method. (d) Compute the volume swept out using the your choice of the integrals in (b) or (c). 3. A bug travels along a curve C . It±s position at time t is given by the following parametric equations x = t cos t; y = 1 sin t; 0 ± t ± 2 : Find the distance traveled by the bug. 4. Find the length of the graph of y = e 2 x e 2 x for 0 ± x ± 1 : 5. Consider the di²erential equation dy dx = 3 x 2 y 2 : (a) Find the general solution.
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Unformatted text preview: y (1) = 2 : 6. A potato comes out of an oven with an internal temperature of 212 degrees Fahreneight. Ten minutes later it has cooled to 140 degrees F. Assuming the room temperature is 70 degrees F, how long does it take to cool to 90 degrees F? 7. A cylindrical tank has radius three feet and length 10 feet. It is buried horizontally below a gasoline station (its axis of symmetry is horizonal. It is half full of gasoline weighing 47.4 pounds per cubic foot. How much work is required to pump its contents though an outlet ten feet above the center of the tank? 8. A 50 foot chain weighing 1.5 pounds per linear foot dangles from the side of a ship. How much work is required to raise it to the level of the deck. (Assume the top link of the chain is at deck level.) 1...
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