200pj2

# 200pj2 - map. (iii) If you start to move on the surface...

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Math 200 Fall, 2006 Project #2 Instructions: Use your knowledge of Maple commands to obtain your solutions. Include explanations of how you obtain your answers, and illus- trate your work with graphs whenever appropriate. Try to answer ques- tions in a clear, direct, and eﬃcient way. 1. Consider the function z = f ( x, y ) = x 3 + 2 xy . (a) Plot the level curves of the function for z = - 2, z = - 1, z = 0, z = 1, and z = 2. Label each curve clearly. (b) Imagine the surface whose height above any point ( x, y ) is given by z = f ( x, y ). Suppose you are standing on that surface at the point where x = 1, and y = 2. (i) What is your height. (ii) Does your height increase or decrease if you start to move on the surface parallel to the x -axis in the direction of increasing x ? Justify your answer using a contour
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Unformatted text preview: map. (iii) If you start to move on the surface parallel to the y-axis in the direction of increasing y , does your height increase or decrease? Justify your answer using a cross-section of f ( x, y ). 2. Investigate the intersection of the surfaces z = p x 2 + y 2 and z = 6-x 2-y 2 . Your solution should include a sketch, a word description, and a simpliﬁed equation for the intersection. 3. Evaluate the following limit, or show that it does not exist. lim ( x,y ) → (0 , 0) sin( x ) sin 3 ( y ) 1-cos( x 2 + y 2 ) 4. Can the function f ( x, y ) = xy ( x 2-y 2 ) x 2 + y 2 be deﬁned at (0 , 0) in such a way that it becomes continuous there? If so, how?...
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## This note was uploaded on 03/28/2011 for the course APSC 254 taught by Professor Stephen during the Spring '11 term at UBC.

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