# 1696 - MATH 203 FINAL EXAMINATION SPRING 2005 PART I:...

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MATH 203 FINAL EXAMINATION SPRING 2005 PART I: Answer ALL questions in this part (10 points each) Show all work and simplify all answers. NO CALCULATORS!!! 1 . (a) Sketch the graph of x 2 4 + y 2 4 + z 2 64 = 1. Also graph the traces of this graph in the xy - and xz -planes. (b) Find an equation of the tangent plane at the point (1 , - 1 , 4 2) to the graph in Part (a). 2 . For the line with parametric equations x = 3 + t y = 2 + 2 t z = - 1 - 3 t and the plane with equation z = x +2 y : (a) Show the line is not perpendicular to the plane. (b) Find the point of intersection. (c) Find the symmetric form of the equations of the line which is perpendicular to the above plane and which passes through the z -axis at z = 4. 3 . Evaluate ± R x 2 y dx dy , where R is the planar region bounded by y = x 2 and y = 4. 4 . For the function f ( x, y, z )= e - xyz + x , ±nd: (a) The directional derivative at (2 , 0 , 1) in the direction v =3 i + j + k . (b) (i) The direction and (ii) the magnitude of greatest increase at (2

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## This note was uploaded on 10/29/2011 for the course MATH 190 taught by Professor Ocken during the Spring '11 term at CUNY City.

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1696 - MATH 203 FINAL EXAMINATION SPRING 2005 PART I:...

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