quiz1_sol - Give the equations of the cross-sections of the...

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Date: Jan 19, 2011 MA3160-08 Quiz 1 No Calculators! Justify all answers! Name (print): Solutions 1. (5pts.) Find the equation of the set of points whose distance from the z-axis equals the distance from the xy-plane. Solution The points with distance d from the z-axis are given by d = p x 2 + y 2 . The points with distance d from the xy-plane are given by d = | z | . Equating the two expressions gives | z | = p x 2 + y 2 or z 2 - x 2 - y 2 = 0 Note that this is a (double) cone whose tip is at the origin and whose axis coincides with the z-axis. 2. (5pts.)
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Unformatted text preview: Give the equations of the cross-sections of the function f ( x , y ) = y 2 + 1 when x = 1 and when y =-1. This is a parabolic cylinder, whose equation is independent of x . Therefore, the equations of the two cross-sections are x = 1 : f (1 , y ) = y 2 + 1 and y =-1 : f ( x ,-1) = 2 Note that the x = const . cross-sections have all the same equations z = y 2 + 1, and f ( x ,-1) = 2 is the horizontal line z = 2 in the y =-1 plane....
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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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