Assignment 1

Assignment 1 - d) lim ( x,y ) (0 , 0) | x |-| y | | x | + |...

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Math 237 Assignment 1 Due: Friday, Sept 19th 1. For each of the following function f : R 2 R i) Sketch the domain of f and state the range of f . ii) Sketch level curves and cross sections. iii) Sketch the surface z = f ( x, y ). a) f ( x, y ) = x 2 - y 2 + 1. b) f ( x, y ) = p x 2 + y 2 2. Find the limit, if it exists, or show that the limit does not exist. a) lim ( x,y ) (0 , 0) x 4 + y 4 x 2 + y 2 b) lim ( x,y ) (0 , 0) 2 x 2 + x 2 y +2 y 2 x 2 +2 y 2 c) lim ( x,y ) (0 , 0) x 2 y 3 x 4 - 2 y 6
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Unformatted text preview: d) lim ( x,y ) (0 , 0) | x |-| y | | x | + | y | 3. Let f ( x, y ) = p x 2-y 2 a) Sketch the domain of f . b) Explain why lim ( x,y ) (0 , 0) f ( x, y ) does not exist. c) How could we modify the denition of a limit so that the limit in b) exists? What would be the value of the limit? 1...
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This note was uploaded on 01/04/2012 for the course MATH 237 taught by Professor Wolczuk during the Spring '08 term at Waterloo.

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