212_Practicetest1

# 212_Practicetest1 - Test 1: Math 212 Practice Exam This is...

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Test 1: Math 212 Practice Exam This is a practice exam for Math 212 Exam I, Spring 2008. It is LONGER than the in class exam will be, but should give you a good idea for the standard types of problems and diﬃculty level that will be on the exam. Problems like these will constitute roughly 80% of the exam. The rest of the exam will consist of problems that you have not seen before. Let me know if you see any typos or incorrect solutions!! 1

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Problem 1 Find an equation of the plane in R 3 which is tangent to the surface x 3 - 2 y 3 + xz 2 = 0 at the point (1 , 1 , 1) . The surface is the level surface given by g ( x,y,z ) = x 3 - 2 y 3 + xz 2 = 0. The gradient is g = (3 x 2 + z 2 , - 6 y, 2 xz ). Therefore, g (1 , 1 , 1) = (4 , - 6 , 2) is the normal vector to the surface. The equation of the plane is given by (4 , - 6 , 2) . ( x - 1 ,y - 1 ,z - 1) = 4 x - 6 y + 2 z = 0 . Problem 2 Sketch the level curves for the function f ( x,y ) = 2 - x 2 - y 2 for c = - 1 , 0 , 1. Solution: Concentric circles of radius 3 , 2 , 1 all centered at the origin. Problem 3
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## This note was uploaded on 10/04/2010 for the course MATH 166 taught by Professor Hotlz during the Spring '08 term at HCCS.

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212_Practicetest1 - Test 1: Math 212 Practice Exam This is...

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