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Unformatted text preview: =  r ( t ) r 00 ( t )   r ( t )  3 . Proof. The key point is to remember that the parametric equations of the ellipse can be chosen to be x = 3 cos t,y = 2 sin t or x = 3 sin t,y = 2 cos t . Consider the vector function r ( t ) = < 3 cos t, 2 sin t, >,t R As (3 cos t ) 2 9 + (2 sin t ) 4 = 1 and z = 0, then r ( t ) is the right vector function representing the ellipse on the xyplane. The point (0 , 2) corresponds to r ( / 2). r ( t ) = <3 sin t, 2 cos t, >, then r ( / 2) = <3 , , > . r 00 ( t ) = <3 cos t,2 sin t, >, then r 00 ( / 2) = < ,2 , > . As  r ( / 2)  = 3, and r ( / 2) r 00 ( / 2) = 6 k then = 6 3 3 = 2 9 ....
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This note was uploaded on 02/27/2011 for the course MATH 101 taught by Professor Y during the Spring '11 term at Columbia College.
 Spring '11
 Y
 Calculus

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