OldExam4

# OldExam4 - MATH 2008/09B WINTER 2007 AN OLD FINAL EXAM 1...

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AN OLD FINAL EXAM 1. Find a scalar(cartesian) equation of the plane that contains the point (1 , 1 , 1) and the line x + 1 1 = y 2 2 = z + 3 3 . 2. Find the value(s) of c such that the lines v r 1 = (1 , 6 , 3) + t (1 , 1 , c 2 ) and v r 2 = (2 , 1 , 4) + s (1 , 3 , 1) intersect. 3. Let the space curve C : r ( t ) = ( t ) v i + ( t 2 1 ) v j +( t ) v k be given and let the point P (1 , 0 , 1) lie on C ; (a) Find the unit tangent vector to the curve C at the point P ; (b) Find the tangential and normal components of the acceleration vector at the point P ; (c) Use (a) and (b) to ±nd the unit normal vector at the point P ; (d) Find the unit binormal vector at the point P . 4. Given the function f ( x, y, z ) = e x 2 + y 2 + z 2 1 x 2 + y 2 + z 2 if ( x, y, z ) n = (0 , 0 , 0) and f (0 , 0 , 0) = 1; (a) Determine if lim ( x,y,z ) (0 , 0 , 0) f ( x, y, z ) exists. If it does, ±nd the limit. Justify your answer by appealing to a theorem or other means;

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OldExam4 - MATH 2008/09B WINTER 2007 AN OLD FINAL EXAM 1...

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