253fin - Name MATH 253 Sections 501-503,200 Final Exam Sec...

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Name Sec MATH 253 Final Exam Fall 2008 Sections 501-503,200 P. Yasskin Multiple Choice: (5 points each. No part credit.) 1-10 / 50 12 / 25 11 / 15 13 / 15 Total / 105 1 . Find a parametric equation of the line tangent to the curve r u ( u 29 = ( 2sin u ,2cos u , u 29 at the point ( 0, - 2, U 29 . a . X ( t 29 = (- 2, - 2 t ,1 + U t 29 b . X ( t 29 = ( 0, - 2 t - 2, U + t 29 c . X ( t 29 = (- 2 t , - 2, U + t 29 d . X ( t 29 = (- 2 t - 2,0, U + t 29 e . X ( t 29 = ( 0, - 2 t - 2,1 + U t 29 2 . The density of the fog is given by ± = 30 - x 2 - y 2 - z . If an airplane is at the position ( x , y , z 29 = 2 ,2,4 , in what unit vector direction should the airplane initially travel to get out of the fog as quickly as possible? a . - 2 2 5 , - 4 5 , - 1 5 b . 2 2 5 , 4 5 , 1 5 c . - 2 10 , - 2 10 , - 2 10 d . 2 10 , 2 10 , 2 10 e . - 2 10 , 2 10 , 2 10 1
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3 . Find an equation of the plane tangent to the graph of the function z = x 2 y + xy 2 at the point ( 2,1 29 . a
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253fin - Name MATH 253 Sections 501-503,200 Final Exam Sec...

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