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Unformatted text preview: f (-22,45). 4. Consider f ( x , y ) = p 1-x 2-y 2 . (a) What is the domain of f ? That is, for which ( x , y ) does the function make sense? (b) Describe geometrically the surface which is the graph of f . (c) Find the tangent plane to the graph at ( x , y ) = (1/2,1/2). (d) Consider the vector v = ( 1/2,1/2,1/ p 2 ) which goes from to the point on the graph where we just found the tangent plane. What is the angle between v and a normal vector to the tangent plane? 5. Consider f ( x , y ) = 3 p x 3 + y 3 . (a) Compute f x (0,0). Note: this partial derivative exists. (b) Is f differentiable at (0,0)?...
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This note was uploaded on 02/20/2011 for the course MATH 241 taught by Professor Kim during the Fall '08 term at University of Illinois, Urbana Champaign.
- Fall '08