a1 - f . ii) Sketch some level curves and cross sections of...

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Math 237 Assignment 1 Due: Friday, Jan 14th * 1. Let f ( x,y ) = | 1 - x 2 - y 2 | . i) Sketch the domain of f and state the range of f . ii) Sketch some level curves and cross sections of f ( x,y ). * 2. Let f ( x,y ) = p x 2 - y 2 . a) Sketch the domain and state the range of f . b) Sketch some level curves and cross sections of f ( x,y ). c) Print a Maple plot of the surface z = p x 2 - y 2 . Draw the level curve 1 = p x 2 - y 2 and the cross-section z = x 2 - 0 2 on your print out. 3. For each of the following functions f : R 2 R i) Sketch the domain of f and state the range of
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Unformatted text preview: f . ii) Sketch some level curves and cross sections of f ( x,y ). iii) Sketch the surface z = f ( x,y ). Verify your answer using Maple. (If you plot the surface in Maple before attempting to sketch the surface, you are missing the point of the exercise). a) f ( x,y ) = p 4 + x 2-y 2 . b) f ( x,y ) = x 2 . c) f ( x,y ) = p | 1-x 2-y 2 | . NOTE: Only * questions will be graded 1...
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This note was uploaded on 12/05/2011 for the course MATH 237 taught by Professor Wolczuk during the Winter '08 term at Waterloo.

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