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tut5 - d Based on your answer in c what can you conclude...

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Math 237 Tutorial 5 Problems Wed, Oct 22/08 Midterm Prep 1: Sketch the level curves and cross sections of f ( x, y ) = ( x - y ) 2 . 2: Determine if each of the following limits exist. Evaluate the limits that exist. a) lim ( x,y ) (1 , 1) x 2 / 3 y 4 / 3 x 2 + y 2 . b) lim ( x,y ) (0 , 0) | x | 5 / 2 + | y | 5 / 2 x 2 + y 2 . 3: Let f ( x, y ) = x 2 y - 3 y 3 2 x 2 + y 2 if ( x, y ) 6 = (0 , 0) 0 if ( x, y ) = (0 , 0) . a) Find L (0 , 0) ( x, y ). b) Determine if f is continuous at (0 , 0). c) Determine all points where f is differentiable.
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Unformatted text preview: d) Based on your answer in c) what can you conclude about the continuity of both f x and f y ? e) Find the rate of change of f in the direction of (0 , 1) and (1 , 1). 4: Let f ( x,y ) = g ( u,v ), where u = x 2-y 2 and v = 2 xy . Find f xx + f yy stating any assumptions you need to make about g ....
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