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OldExam2 - MATH 2008/09A FALL 2005 AN OLD FINAL EXAM 1....

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MATH 2008/09A FALL 2005 AN OLD FINAL EXAM 1. Find the intersection of the plane π : x + y +2 z = 18 and the line L : x 1 1 = y 2 2 = z 3 3 . 2. (a) Find the angle between two planes π 1 : x z + 7 = 0 and π 2 : 2 x + y z + 8 = 0. (b) Find the area of the triangle with two sides vu = (1 , 2 , 2) and vV = ( 1 , 3 , 0). 3. Let the plane curve C : y = e x be given and the point P (0 , 1) lies on C ; (a) Verify that the curvature of C at the point P is 1 2 2 ; (b) Find the radius of the Osculating circle at the point P ; (c) Find the coordinates of the center of the Osculating circle at the point P . 4. Given the function h ( x, y, z ) = ( x 2 + y 2 + z 2 ) ln( x 2 + y 2 + z 2 ) if ( x, y, z ) n = (0 , 0 , 0) and h (0 , 0 , 0) = ln 2; (a) Determine if lim ( x,y,z ) (0 , 0 , 0) h ( x, y, z ) exists. If it does, ±nd the limit. Justify your answer by appealing to a theorem or other means; (b) Is h continuous at (0 , 0 , 0)? Why? (c) Find the largest set on which

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This note was uploaded on 05/26/2010 for the course MATH Math2008 taught by Professor Monadi during the Fall '08 term at Carleton.

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OldExam2 - MATH 2008/09A FALL 2005 AN OLD FINAL EXAM 1....

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