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Unformatted text preview: Name: PID: Discussion Section No: Time: TAs name: Quiz 2, Math 20C - Lecture D (Fall 2007) Duration: 20 minutes Please close all your notes and books, turn off your phones and put them away. To get full credit you should support your answers. 1. (5 points) Find a parametric equation for the tangent line to the curve with the parametric equation x = e- t cos t, y = e- t sin t, z = e- t at the point (1 , , 1). Solution. For t = 0, the point on the curve is ( e cos 0 , e sin 0 , e ) = (1 , , 1). The direction of the tangent line to the curve x = e- t cos t, y = e- t sin t, z = e- t is given by the value of vector ( dx dt , dy dt , dz dt ) (1) when t = 0. The direction (1) is ( dx dt , dy dt , dz dt ) = ( e- t ( sin t cos t ) , e- t ( sin t + cos t ) , e- t ) (2) When t = 0, this equals ( 1 , 1 , 1 ) . Thus, the tangent line at (1 , , 1) has direction ( 1 , 1 , 1 ) ....
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- Fall '08