# Review 2 - MAC 2313 SUMMER 2010 Test 2 Review 1 Find and...

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Unformatted text preview: MAC 2313 SUMMER 2010 Test 2 Review 1) Find and sketch the domain for the following functions. (a) f ( x,y ) = √ 1- x 2- p 1- y 2 (b) f ( x,y,z ) = ln(16- 4 x 2- 4 y 2- 4 z 2 ). 2) Describe in words or sketch the graph of the following functions. (a) f ( x,y ) = 10- 4 x- 5 y . (b) f ( x,y ) = 4 x 2 + y 2 + 1. (c) f ( x,y ) = x 2 + 1. 3) Find the limit, if it exists, or show that the limit does not exist. (a) lim ( x,y ) → (0 , 0) xy 3 x 2 + y 6 (b) lim ( x,y ) → (2 , 1) 4- xy x 2 + 3 y 2 (c) lim ( x,y ) → (0 , 0) xy 3- yx 3 x 2 + y 2 4) Discuss the continuity of the functions in question 3 (b) at the point (2 , 1) and the function ˜ f ( x,y ) = xy 3- yx 3 x 2 + y 2 if ( x,y ) 6 = (0 , 0) 1 if ( x,y ) = (0 , 0) at the point (0 , 0). 5) Use Polar coordinates ( x = r cos θ , y = r sin θ ) to find the limits of the following functions. (a) lim ( x,y ) → (0 , 0) sin( x 2 + y 2 ) x 2 + y 2 (b) lim ( x,y ) → (0 , 0) ( x 2 + y 2 )ln( x 2 + y 2 ) 6) Find the first order partial derivatives of the following functions.6) Find the first order partial derivatives of the following functions....
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Review 2 - MAC 2313 SUMMER 2010 Test 2 Review 1 Find and...

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