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Unformatted text preview: MATH 30101 Quiz #2 Solutions 1. (5 points) Classify the surface described by the equation x 2 + 4 y 2 3 z 2 6 x + 8 y + 12 z = 10 ; if applicable, identify its center and orientation. Completing the square gives the equation x 2 6 x + 9 + 4 y 2 + 8 y + 4 3 z 2 + 12 z 12 = 10 + 9 + 4 12 ( x 3) 2 + 4( y + 1) 2 3( z 2) 2 = 11 so this surface is a hyperboloid of one sheet, oriented in the zdirection, with a center as (3 , 1 , 2). 2. (6 points) Find the arclength of the curve described by r ( t ) = ( t 2 2 t ) i + 8 3 t 3 / 2 j between the values t = 0 and t = 4 . Note that r ( t ) = (2 t 2) i + 4 t j , so  r ( t )  = q (2 t 2) 2 + (4 t ) 2 = 4 t 2 8 t + 4 + 16 t = 4 t 2 + 8 t + 4 = 2 t + 2 And then the arclength is given by the integral Z 4  r ( t )  dt = Z 4 2 t + 2 dt = t 2 + 2 t 4 = 16 + 8 (0 + 0) = 24 3. (5 points) Find an equation (in either parametric or symmetric form) for the line tangent to the curve described by r ( t ) = h 6 t, t 2 3 , 4...
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This note was uploaded on 01/12/2012 for the course MATH 301 taught by Professor Staff during the Fall '08 term at University of Louisville.
 Fall '08
 Staff
 Completing The Square

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