OldExam6 - MATH 2008/09A Fall 2007 AN OLD FINAL EXAM (II)...

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MATH 2008/09A Fall 2007 AN OLD FINAL EXAM (II) 1. Determine whether or not the point A (8 , 0 , 3) lies on the line L with vector equation v r = (0 , 8 , 4) + t (2 , 3 , 1). 2. Find a scalar (cartesian) equation of the plane that is parallel to the line of intersection of the planes π 1 : x + 2 y 4 z = 7 and π 2 : 2 x 2 y 5 z = 10, and contains the line L : x = t,y = 1 + t,z = 2 t . 3. Let the plane curve C : y = cos x be given and the point P (0 , 1) lies on C ; (a) Find the curvature of the curve C at the point P ; (b) Find the unit tangent vector to the curve C at the point P ; (c) Find the unit normal vector to the curve C at the point P ; (d) Find the equation of the osculating circle at the point P . 4. Given the function f ( x,y ) = ( x 1) 2 ln x ( x 1) 2 + y 2 if ( x, y ) n = (1 , 0) and f (1 , 0) = 1; (a) Determine if lim ( x,y ) (1 , 0) f ( x,y ) exists. If it does, ±nd the limit. Justify your answer; (b) Is f continuous at (1 , 0)? Why? (c) Find the largest set on which
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OldExam6 - MATH 2008/09A Fall 2007 AN OLD FINAL EXAM (II)...

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