Fall 2007 - Hohnhold's Class - Quiz 2 (Version B)

# Fall 2007 - Hohnhold's Class - Quiz 2 (Version B) - x and...

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Quiz 2 for Math 20B. Fall Quarter 2007, UCSD Henning Hohnhold Name: Section: #1: #2: Total: (1) (5 points) Please sketch the region enclosed by the curves x + y 2 - 2 y = 0 and - x + y = 2 and compute its area. The sketch looks like this: -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -1 -0.5 0.5 1 1.5 2 2.5 The area is given by Z 2 - 1 2 y - y 2 - ( y - 2) dy = 9 2

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(2) (5 points) Sketch the ellipse given by the equation 1 4 x 2 + y 2 = 1 . (Hint: Find the intersection points with the
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Unformatted text preview: x- and y-axes ﬁrst.) Compute the volume of the solid obtained by revolving the ellipse around the y-axis. The sketch looks like this:-2-1.6-1.2-0.8-0.4 0.4 0.8 1.2 1.6 2-1.6-1.2-0.8-0.4 0.4 0.8 1.2 The resulting volume is given by π Z 1-1 p 4-(2 y ) 2 2 dy = π Z 1-1 4-(2 y ) 2 dy = 16 3 π 2 Good Luck! 3...
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Fall 2007 - Hohnhold's Class - Quiz 2 (Version B) - x and...

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