a1 - . c) lim ( x,y ) (0 , 0) x 2 y 3 x 4 + y 6 . d) lim (...

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Math 237 Assignment 1 Due: Friday, Sept 25th 1. For each of the following functions 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 . b) f ( x,y ) = p | 1 - 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 2 - y 2 x 2 + y 2 . b) lim ( x,y ) (0 , 0) y 2 - 4 | y |- 2 | x | | x | +2 | y |
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Unformatted text preview: . c) lim ( x,y ) (0 , 0) x 2 y 3 x 4 + y 6 . d) lim ( x,y ) (0 , 0) x 4 y 5 x 8 + y 6 . 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. 1...
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