OldExam5 - MATH 2008/09A Fall 2007 AN OLD FINAL EXAM (I) 1....

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MATH 2008/09A Fall 2007 AN OLD FINAL EXAM (I) 1. Find parametric equations of the line passing through the origin and parallel to the line of intersection of the planes x + 2 y z = 2 and 2 x y + 4 z = 5. 2. Find the distance between the parallel planes 2 x 2 y z = 12 and 4 x +4 y +2 z = 3. 3. A particle has the acceleration a ( t ) = ( e t , 0 , e t ). Let the initial velocity and initial position vectors be v(0) = (1 , 2 , 1) and r (0) = (1 , 0 , 1) respectively; (a) Find the velocity and the position functions of the motion; (b) Find the unit tangent vector T at the point (1 , 0 , 1); (c) Find the tangential and normal components of the acceleration vector at the point (1 , 0 , 1); (d) Use (b) and (c) to ±nd the unit normal vector at the point (1 , 0 , 1); (e) Find the binormal vector at the point (1 , 0 , 1). 4. Find lim ( x,y ) (0 , 0) xy 3 x 2 + y 2 if it exists, or show that the limit does not exist. 5.
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OldExam5 - MATH 2008/09A Fall 2007 AN OLD FINAL EXAM (I) 1....

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