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MAC 2312 Exam 4 Spring 2011 Key

MAC 2312 Exam 4 Spring 2011 Key - r — 2(1 —sinO 2(ffl...

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2. a; = e* 1, y = e 2t x~- (a) Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. i** U-f-t 3. Find the area of the surface obtained by rotating the curve about the y-axis. y = l - x 2 , 0 < z < l ~ Let w L 3 JJ)
4. (a) Sketch the curve given by the polar equation r = 2(1 sinfl). ~ 2 y (b) Find the area enclosed by r — 2(1 sinO). 2. (ffl t (• J

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Unformatted text preview: r — 2(1 —sinO). 2. (ffl t (• J 5. x = t — e*. y = t + e t \&) Find &. i-e (b) Find g. Oft (c) For which values of t is the curve concave up? I . e . 6. Find tw T o other pairs of polar coordinates of the point (— 1, — ^j-), one with r > 0 and one with r < 0. Then find the Cartesian coordinates of the point. ; VJ-V cr <(-\-. f >(«-T- I...
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