MATH_200_spring_07_exam_3_with_solutions

MATH_200_spring_07_exam_3_with_solutions - 1 , , 6 P . Page...

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Page 1 of 6 Exam Three MATH 200 Spring, 2007 Name_______________________________ Section____________ Show all your work on the exam paper, legibly and in detail, to receive full credit. No Calculators. Page 1) _ 2) _ 3) _ 4) _ 5) _ 6) _ Total 1. (20 points) Use the appropriate form of the multi-dimensional chain rule (MDCR) to find t z and s z . You must use the MDCR to obtain full credit. s y st x e z y x 1 , ; 2
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Page 2 of 6 2. (20 points) Find a unit vector in the direction in which 2 3 4 , y x y x f increases most rapidly at 1 , 1 P , and find the rate of change of f at P in that direction.
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Page 3 of 6 3. (20 points) Find an equations for the tangent plane and parametric equations for the normal line to the line to the surface x e z y 3 sin 3 at the point
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Unformatted text preview: 1 , , 6 P . Page 4 of 6 4. (20 points) Locate all relative maxima, relative minima, and saddle points, if any. 3 2 3 , 2 x y xy y y x f Page 5 of 6 5. (5 points) Find the normal vector for the paraboloid 2 2 y x z at the point (1, -1, 2). (5 points) Find the normal vector for the ellipsoid 9 4 2 2 2 z y x at the point (1, -1, 2). (10 points) Find the parametric equations for the tangent line of the curve of intersection of the paraboloid 2 2 y x z and the ellipsoid 9 4 2 2 2 z y x at the point (1, -1, 2). Page 6 of 6 6. (10 points) Consider the following modification of problem 1: s y st x e z y x 1 , ; 2 . Find t z and s z WITHOUT using the chain rule....
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MATH_200_spring_07_exam_3_with_solutions - 1 , , 6 P . Page...

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