SecBEx2W01 - ( , , ) 1 2 1 (2) (b) does this tangent plane...

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EXAM 2 MATH 22 Name: ____________________________ Winter 2001 Section: __________ You must show all work clearly to receive full credit. (8) 1) Find and sketch the domain of the function . f x y x y x y ( , ) ln( ) = + + - - 1 1 2 2 2 2 (10) 2) Determine the largest set on which the function g is continuous. Give your reasoning. g x y xy x xy y ( , ) = + + 2 2 0 if if ( , ) ( , ) ( , ) ( , ) x y x y = 00 00 (6) 3) Find if . z x xyz x y z = + + ln( ) (8) 4) Determine if there exists a function f with and f x y x y x ( , ) cos( ) = + and whose second partial derivatives are continuous. Give your f x y x y y ( , ) sin( ) = - - p 2 reasoning. (10) 5) Is differentiable at (2,2)? If not, give your reasoning. If so, find the f x y x y ( , ) = linearization L(x,y) of f at (2,2). (8) 6) For , show that . f x y xy y ( , ) = + 2 2 x f x y f y f x y + = 2 ( , ) 7) Given the surface , x z y
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Unformatted text preview: ( , , ) 1 2 1 (2) (b) does this tangent plane pass through the origin? Give your reasoning. 8) For , f x y z xyz ( , , ) sin( ) = (8) (a) find the directional derivative of f at (1,1,0) in the direction of D f u r r v k = 99 (4) (b) what is the maximum rate of change of f at (1,1,0) and show that it has the same direction as the vector . r v (16) 9) Find the local maximum and minimum values and saddle point(s) of the function . f x y x xy y ( , ) = - + 3 3 6 8 (12) 10) Use Lagrange multipliers to find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its all edges is a constant, say c....
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SecBEx2W01 - ( , , ) 1 2 1 (2) (b) does this tangent plane...

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