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# 1695 - 1 MATH 203 Final Exam Instructions Complete every...

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1 MATH 203 Final Exam December 18, 2008 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. Proctors will confiscate any devices observed in the examination room. 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) Parameterize the line that passes through the point (4 , 0 , - 3) which is parallel to the intersection of the plane 2 x - y + z = 2 and the plane x - 3 z = 4 (b) Find an equation of the plane perpendicular to the planes 2 x - y + z = 2 and x - 3 z = 4 that passes through (4 , - 2 , 3) . 2. Let f ( x, y, z ) = x 2 y + y 2 z. (a) Evaluate f . (b) Find an equation of the tangent plane to the surface x 2 y + y 2 z = - 1 at the point (2 , - 1 , 3).

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1695 - 1 MATH 203 Final Exam Instructions Complete every...

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