MTh203(exam2review) - MTH203 Review Problems(EXAM#2) Q1....

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MTH203 Review Problems(EXAM#2) Q1. Consider the plane x + y + z = 0. a)Give three distinct points with integer coordinates that lie on this plane. b) Find the area of the triangle formed by the three points. Q2. Suppose u =< 1,0 > , v =< 1 2 , 1 2 > , D u f a , b ±± = 3 and D v f a , b ±± = 2 a) Find 4 f a , b ± b) What is the maximum possible value of D w f a , b ±± = 3 for any w c) Find a unit vector w =< w 1 , w 2 > such that D w f a , b ±± = 0. Q3. Find an equation of the tangent plane to the hyperboloid given by z 2 ? 2 x 2 ? 2 y 2 ? 12 = 0 at the point 1, ? 1, 4 ± . Q4. Find symmetric equations for the tangent line to the curve of intersection of the ellipsoid given by x 2 + 4 y 2 + 2 z 2 = 27 and the hyperboloid given by x 2 + y 2 ? 2 z 2 = 11 at the point (3,-2,1). 5) Let R be the region in the plane bounded by the curves y 2 = 2 x and y 2 = 8 ? 2 x . Set up the R XX f x , y ± dA in both orders dxdy and dydx. Find the area of R. 6) Evaluate the iterated integral by converting to polar coordinates
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This note was uploaded on 10/20/2008 for the course MATHS MTH 203 taught by Professor None during the Spring '08 term at American University of Sharjah.

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