MT2 Spr 07 Ziane

MT2 Spr 07 Ziane - 4 0 3 Problem 3(15 points Let z = f x y...

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Spring 2007 Math 226 EXAM 2 Prof. M. Ziane Please Print: Last name: First Name : Signature: ID# INSTRUCTIONS: 1. NO CALCULATORS ALLOWED AND NO CHEATING PERMITTED. 2. Clearly indicate your fnal answers by circling them. 3. Show all your work. Unsupported answers will not receive credit. 4. In general you do not need to “simpli±y” your answers, but you will need to evaluate simple numbers. 5. Point values are labeled and there are 100 total points possible. Good luck! March 29, 2007 1
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Problem 1. (20 points) Find a) lim ( x,y ) (0 , 0) sin( xy ) x 2 + y 2 b) lim ( x,y ) (0 , 0) x 3 y - y 3 x x 2 + y 2 2
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Problem 2. (15 points) Find an equation of the tangent plane to the surface z = y ln x at the point (1
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Unformatted text preview: , 4 , 0) . 3 Problem 3. (15 points) Let z = f ( x, y ) , where x = r cos θ and y = r sin θ, Find ∂z/∂r and ∂z/∂θ. Problem 4. (15 points) Let f ( x, y ) = x 2 y 3-y 4 . Find the directional derivative of the function f at the point (2 , 1) in the direction of the vector < 3 ,-2 > . 4 Problem 5. (15 points) Find the points on the surface given by x 2 + 2 y 2 + 3 z 2 = 1 where the tangent plane is parallel to the plane 3 x-y + 3 z = 1 . 5 Problem 6. (20 points) Find the extreme values of the function f ( x, y, z ) = xyz where x 2 + 2 y 2 + 3 z 2 ≤ 6 . 6...
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MT2 Spr 07 Ziane - 4 0 3 Problem 3(15 points Let z = f x y...

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