Math 212, Fall 2011Name: __________________________________Exam 21.[18 points (9 pts each)](a) Find the equation of the tangent plane to the surfaceat the point.b
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(b) Find parametric equations for the line tangent to the curveat the point.ra bab> œØ>ß$/ ß/ Ù!ß$ß"sin>#>
Math 212, Fall 2011Exam 222.In the figure to the right, a circle of radius 1 is[10 points]tangent to a perpendicular pair of line segments.Find thecoordinates of the center of the circle.LParen10,0RParen1LParen13,1RParen13.Find the distance from the lineto the plane.
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Math 212, Fall 2011Exam 234.Letbe the plane, and letbe the plane.Find the equation of[10 points]T#B$CD œ&UC$D œ""the plane through the pointthat is perpendicular to bothand.ab"ß#ß$TU
Math 212, Fall 2011Exam 245.[16 points (8 pts each)](a) Evaluate, whereis the region inside the cylinderand between the planesI$##< D.ZIB C œ"D œ!D œ"and(b) Evaluate, whereis the solid hemisphere defined byand.(((.