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m203finspring2010

# m203finspring2010 - 1 MATH 203 Final Exam Instructions...

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1 MATH 203 Final Exam, May 24, 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. No calculators or other electronic devices may be used during the examination. Answers may be left in terms of 7 , sin(3) , π , etc. Give reasons for all answers. This exam will last 2 hours and 15 minutes. Good luck! PART I: Answer all parts of Questions 1-7. Each question is worth 10 points 1. Let P be the plane that contains the points (2 , - 1 , 1), (1 , 3 , 1) and (2 , 1 , 2) and let Q be the plane z = x + y . (a) Parameterize the intersection of the two planes P and Q . (b) What is the smaller of the two angles of intersection of the planes? 2. (a) Parameterize the tangent line to the curve ~ r ( t ) = < 1 2 t , e t 2 , t 1 / 3 > at the point ( - 1 2 , e, - 1). (b) Find an equation of the tangent plane to the surface z = x 2 - 4 y 2 + 3 at the point (2 , - 1 , 3). 3. Find all local maxima and minima and all saddle points of the function f ( x, y ) = x 2 - 4 xy + 6 x - 8 y + 2 y 2 + 10.

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m203finspring2010 - 1 MATH 203 Final Exam Instructions...

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