SecAEx2W01 - (b the equation of the normal line at the...

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EXAM 2 MATH 22 Name: ____________________________ Winter 2001 Section: __________ You must show all work clearly to receive full credit. 1) Find and sketch the domain of the function . f x y y x y x ( , ) ln( ) = - + 2) Determine the set where the function h is continuous and give your reasoning h x y xy x xy y ( , ) = + + 2 2 0 if if ( , ) ( , ) ( , ) ( , ) x y x y = 0 0 0 0 3) Find if . z x xy z x y z 2 2 3 = + + sin( ) 4) Is there a function f whose first partial derivatives are and f x y e y x x ( , ) = + 2 and whose second-order partial derivatives are continuous. Give f x y x y y ( , ) = + 5 2 your reasoning. 5) Is differentiable at the point (e,e)? If not, give your reasoning. If f x y y x ( , ) ln = so, find the linearization L(x,y) of f at (e,e). 6) Given where , , use the Chain Rule to find z y x = 2 cos x t uv = 2 y u tv = + 2 z t when t=2, u=1, v=0. 7) Given the surface , find the following x y z xyz 2 2 2 2 3 4 - - + = (a) the equation of the tangent plane to the surface at the point (3,-2,1)
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Unformatted text preview: (b) the equation of the normal line at the point ( 3, -2, 1). 8) Given , f x y x y ( , ) = + 1 2 (a) find the rate of change of f at the point (1,1) in the direction of the vector r r r v i j = -4 3 (b) in which direction does f change most rapidly at (1,1)? (c) what is the maximum rate of change of f at (1,1)? (9) Find the local maximum and minimum values and saddle point(s) of the function . f x y x x y y ( , ) = + + 2 2 2 10) Given , f x y x y ( , ) = + 2 2 2 (a) use Lagrange multipliers to find the maximum and minimum values of f when x y 2 2 1 + = (b) find the absolute maximum and minimum values of f on the closed and bounded set . D x y x y = + ≤ {( , ) } 2 2 1...
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