20c-wi97-lin-final

# 20c-wi97-lin-final - Final Exam Math 20C Winter 1997 Place...

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Final Exam Math 20C Winter 1997 Place all books, papers under your desk. On the front of your blue book write your name and section number. In a column, number one to ten. Graphing calculators and a 3 × 5 note card is permitted. Turn in the note card with your ﬁnal exam. Box answers and show all your work. Good luck. 1. (a) 10 pts. Find the equation of a plane passing through P =(3 , 2 , 1), Q =(1 , 1 , 1) and R =( - 1 , 2 , 4). (b) 10 pts. Find the equation of a line through (2 , 3 , 7) parallel to the line of intersec- tion of the planes 2 x + y + z = 0 and x - y +7 z =0. (c) 10 pts. Draw several level curves of f ( x, y )= x y . Compute ~ f (1 , 2) and sketch the ~ f (1 , 2) and the level curve passing through (1 , 2). 2. The graph of the surface z = f ( x, y ) is shown in the following ﬁgure. (a) 10 pts. Is the directional derivative of f in the direction ~ i + ~ j positive or negative at (2 , 5)? (b)

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## This note was uploaded on 04/28/2008 for the course MATH 20C taught by Professor Helton during the Spring '08 term at UCSD.

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20c-wi97-lin-final - Final Exam Math 20C Winter 1997 Place...

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