quiz2_sol - g x y = xy 2 e xy 3 Let f x y z = g x y-z-2...

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Date: Jan 26, 2011 MA3160-08 Quiz 2 No Calculators! Justify all answers! Name (print): Solutions 1. (5pts.) Find the equation of the plane whose graph intersects the xz -plane in the line z = 3 x + 4 and intersects the yz -plane in the line z = y + 4. Solution The equation of the plane is z = mx + ny + c . At y = 0: z = 3 x + 0 y + 4 and, therefore, c = 4 and m = 3. At x = 0: z = 0 x + y + 4 which implies n = 1. Therefore, the equation of the plane is z = 3 x + y + 4 2. (5pts.) Find a function f ( x , y , z ) whose level surface f = - 2 is the graph of the function
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Unformatted text preview: g ( x , y ) = xy 2 + e xy + 3. Let f ( x , y , z ) = g ( x , y )-z-2. Then the level surface f ( x , y , z ) =-2 is g ( x , y )-z-2 =-2 which implies z = g ( x , y ). This shows that the desired function is, f ( x , y , z ) = g ( x , y )-z-2 = xy 2 + e xy-z + 1 or, alternatively, f ( x , y , z ) = z-g ( x , y )-2 = z-xy 2-e xy-5...
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This note was uploaded on 04/04/2011 for the course MA 3160 taught by Professor Staff during the Spring '08 term at Michigan Technological University.

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