20c-wi97-lin-mid1

20c-wi97-lin-mid1 - 2 at (1,2) in the direction of ~ + ~...

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Midterm 1 Math 20C Lin 1997 Place all books, papers and calculators under your desk. Write your name and section number on your blue book . In a column number one to four. Box your answers and show all your work. Good Luck! 1. (a) 5 pts. Find 3 complex numbers that satisfy z 3 = i . (b) 5 pts. Find 2 unit vectors that make an angle of π/ 6 with ~ . (c) 5 pts. Find the equation of a plane perpendicular to 2 ~ ı + ~ - ~ k passing through (1 , 2 , 3). (d) 5 pts. P =(2 , - 1 , 0), Q =( - 1 , 0 , 3), R =(2 , 1 , 1) are vertices of a parallelogram. If S is the 4 th vertex opposite P , find S . 2. (a) 10 pts. Let f ( x, y )= x 2 e y + cos( xy ). Let x ( t )= t , y = t 2 . Compute f x f y , f xy . Use the chain rule to find df dt . (b) 10 pts. A function g ( x, y ) has directional derivative 2
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Unformatted text preview: 2 at (1,2) in the direction of ~ + ~ and directional derivative 2 in the direction of ~ + 2 . What is ~ g (1 , 2)? Check your answer. 3. 20 pts. Find all critical points, local maxima, minima and saddle points of f ( x, y ) = xy-x 2-y 2-2 x-2 y + 4. 4. (a) 10 pts. Use Lagrange multipliers to nd the maxima and minima of the function f ( x, y ) = xy subject to the constraint x 2 + y 2 = 1. Find the points where maximum and minimum occur and also the maximum and minimum values of f . (b) 10 pts. Sketch level curves of f and the graph of x 2 + y 2 = 1....
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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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