211finalexam-f08

211finalexam-f08 - b)Determine the equation of the plane...

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CALCULUS 211-FINAL EXAM-DECEMBER 17, 2008 l)Forthe line andtheplane givenbyx : 3 -t, y: t+ | , z:3t andx+y-z: I a)Determine the coordinates of the point of intersection of the line and the plane b)Determine the cosine of the angle between the line and a line normal to the given plane 2)Forthe space curve x : t + L,l : J2t + 1,7 : (t2 - 4) a) Determine the equation of the line tangent to the curve at t : I b) Determine the acceleration vector at t : I 3)Find all the local relative and absolute extrema of the function J(*,y): x2 +3y-3xy boundedbytheregion y: x, !:0, x:2 4)Using Lagrange multipliers find the maximum and minimum values of the function J(*,y) : x€r subject to the constraint x2 + yz : 2 5)a)Determine the directional derivative of .f : e4'+" at the point (1,-1,1) in the direction from (1,3,1)
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Unformatted text preview: b)Determine the equation of the plane tangent to the surface exv+z - | at the point (1,-l,l) 6)Evaluate, using cylindrical coordinates ![!e"aV forthe region between z :0 andz: -the cylinder x2 + /2 : 3 7)Evaluate the line integral [,*rdt where C is the straight line segment from (1,0,1) to (2,-2,2) 8)For the conservative vector field F : 2xyi + (x2 - l)j determine its potenti alflx,y) and evaluate the line integr.t ill,j] F . dr . 9)Evaluate directly as a line intergral f *dy for the closed cuve which encloses the region formed by the curves / : x2 and y : 4 , oriented counterclockwise 10)Use Green's Theorem for the vector field F : (y3 - lnx)i + dV + t + 3x)j to evaluate the line integral ff . a, over the boundary of the region formed by the curves x : y2 and x : 4, as a double integral over this region, oriented counterclockwise and outside 4 - x 2...
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This note was uploaded on 03/30/2012 for the course MATH 211 taught by Professor But during the Spring '08 term at NJIT.

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