m203finfall2010 - 1 MATH 203 Final Exam December 20, 2010...

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1 MATH 203 Final Exam December 20, 2010 Instructions: Complete every question in Part I (Questions 1-7.) Complete three of the five questions in Part II (Questions 8-12). Each question is worth 10 points. PART I: Answer all parts of Questions 1-7. Each question is worth 10 points 1. Let P be the plane that contains the line x = 2 + 3 t,y = - 2 - t,z = 1 - 2 t and the point (2 , - 3 , 1). (a) Give an equation for the plane P . (b) Find the distance of the plane P from the origin. 2. Let f ( x,y,z ) = x 2 y 3 + e x + z - 2 y sin z . (a) Find the directional derivative of f ( x,y,z ) at (0 , 1 , 0) in the direction toward the point (3 , 5 , - 12) (b) Find ∂z ∂x , if z is defined implicitly as a function of x and y by the equation f ( x,y,z ) = 1. (c) Find an equation of the tangent plane to the surface f ( x,y,z ) = 1 at the point (0 , 1 , 0). 3. Find all local maxima and minima and all saddle points of the function f ( x,y ) = 3 x 2 - 6 xy + y 3 - 9 y . 4. Evaluate
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m203finfall2010 - 1 MATH 203 Final Exam December 20, 2010...

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