m203finspring2011 - 1 MATH 203 Final Exam Instructions...

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1 MATH 203 Final Exam, May 19, 2011 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. if needed. 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. (a) Find parametric equations for the line which passes through the point (1 , - 2 , 3) and is parallel to both of the planes 3 x + y + 5 z = 4 and z = 1 - 2 x . (b) Are the two planes in (a) perpendicular to each other? Show the calculation to support your answer. (c) Find the point at which the line you found in (a) intersects the yz -plane. 2. Let f ( x, y, z ) = x + 2 y + e y - 2 x + z 2 . (a) Find the rate at which f is changing at (1 , 2 , 0) in the direction h 3 , 4 , 5 i . (b) Find ∂y ∂x when y is the function of x and z defined implicitly by the equation f ( x, y, z ) = 1.
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