a2 - a) lim ( x,y ) (0 , 0) | x |-| y | | x | + | y | . b)...

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Math 237 Assignment 2 Due: Friday, Jan 21st * 1. Find the limit, if it exists, or show that the limit does not exist. a) lim ( x,y ) (1 , 2) ( x - y ) 2 | x | + | y | b) lim ( x,y ) (0 , 0) x 2 - 2 | x |- 2 | y | 2 | x | + | y | c) lim ( x,y ) (0 , 0) x 3 y 2 x 4 + y 6 * 2. Let f ( x,y ) = ( x 2 - y 2 x 2 + y 2 if ( x,y ) 6 = (0 , 0) 0 if ( x,y ) = (0 , 0) . Determine all points where f is continuous. * 3. Let f ( x,y ) = | x | a | y | b | x | c + | y | d where a , b , c , and d are positive numbers. Prove that if a c + b d > 1, then lim ( x,y ) (0 , 0) f ( x,y ) exists and equals zero. 4. Find the limit, if it exists, or show that the limit does not exist.
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Unformatted text preview: a) lim ( x,y ) (0 , 0) | x |-| y | | x | + | y | . b) lim ( x,y ) (0 , 0) x 2-3 | x |-3 | y | | x | + | y | . c) lim ( x,y ) (0 , 0) x 5 y 2 x 10 + y 4 . d) lim ( x,y ) (0 , 0) x 3 y 4 x 6 + y 6 . NOTE: Only * questions will be graded...
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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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