Unformatted text preview: 0) and f (0 , 0) = 0 . Show that f is continuous at (0 , 0). 4) Let g : R 2 → R be given by g ( x, y ) = x 2 y 3 x 4 + y 4 for ( x, y ) 6 = (0 , 0) and g (0 , 0) = 0 . Determine whether g is continuous at (0 , 0). 5) For each function f , determine whether or not lim ( x,y ) → (0 , 0) f ( x, y ) exists. Determine f (0 , 0) so that f is continuous at (0 , 0), whenever this is possible: a) f ( x, y ) = xy 2 x 2 + 3 y 2 , ( x, y ) 6 = (0 , 0), b) f ( x, y ) = xy 2 x 2 + 2 y 2 , ( x, y ) 6 = (0 , 0)....
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 Spring '08
 WOLCZUK
 Calculus, Continuity, Limits, Continuous function, typical level curves, exceptional level curves

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