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SecBEx2W01

# SecBEx2W01 - 1 2 1(2(b does this tangent plane pass through...

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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 = 0 0 0 0 (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 2 2 2 + = (8) (a) find the equation of the tangent plane to the surface at the point

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