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T2 Practice Problems_1

T2 Practice Problems_1 - Test 2 Practice Problems I suggest...

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Test 2 Practice Problems I suggest looking over the Test 2 Review sheet before attempting these problems. It will help you get a better feel for what you know and what you need to work on. Area Between Curves 1. Find the area between the curve y = 1 /x and the x -axis from x = 1 to x = 2. 2. Find the area of the ”triangular” region bounded on the left by x + y = 2, on the right by y = x 2 , and above by y = 2. 3. Find the area between f ( x ) = x 3 - 3 x 2 and the x -axis. 4. Find the area between x = 4 - y 2 and x = 0. 5. Find the area of the ”triangular” region bounded on the left by y = x , on the right by y = 6 - x , and below by y = 1. 6. You absolutely want to know how to do the last problem on the 5.7 Worksheet . Make sure you understand how to deal with regions that have two different functions bounding them on one side. Cross-Sectional Volumes Find the volume of the following solids. 1. The solid lies between planes perpendicular to the x -axis at x = - 1 and x = 1. The cross-sections perpendicular to the x -axis are circular disks whose diameters run from the parabola y = x 2 to the parabola y = 2 - x 2 . 2. The solid lies between planes perpendicular to the x -axis at x = - 1 and x = 1. The cross-sections perpendicular to the x -axis between these planes are squares whose diagonals run from the semicircle y = - 1 - x 2 to the semicircle y = 1 - x 2 .

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