Math16B - Spring 08 Final Review

Math16B - Spring 08 Final Review - Math 16B Final Review 1...

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Unformatted text preview: Math 16B Final Review May 13, 2008 1.) For each of the following functions, find their relative max- ima, minima and saddle points: a. ) f ( x, y ) = x 4 + y 4- 4 x- 64 y b. ) f ( x, y ) = ye x + 4 y 2- 20 x c. ) f ( x, y ) = x 2 + 6 xy + 3 y 2 + 2 x 2.) Lagrange multipliers: a. ) Find the maximum value of f ( x, y, z ) = 3 x +5 y + z- x 2- y 2- z 2 subject to the constraint 6- x- y- z = 0 b. ) Find the point ( x, y, z ) which minimizes 2 x 2 + 2 y 2 + 2 z 2 + xy subject to the constraint x + y + z = 3 3.)Find the line y = Ax + B which best fits the data points (0 , 1) , (1 , 2) , (2 , 4) 4.) a. ) Let R = { ( x, y ) : q sin( x ) ≤ y ≤ √ x, ≤ x ≤ 1 } . Calculate Z Z R xydydx . b. ) Let R = { ( x, y ) : 0 ≤ y ≤ e x 3 +2 x 2 , 2 ≤ x ≤ 5 } . Calculate Z Z R ( x 2 + 4 x/ 3) dxdy . 5.) Calculate the following integrals: a. ) Z ln( x 2 + 4 x + 4) dx b. ) Z x ( e 2 x + sin (4 x )) dx c. ) Z π/ 6 x sec 2 ( x ) dx 1 d. ) Z 2 x cos( x 2 ) sin(sin( x 2 )) dx 6.) a. ) Use the trapezoidal rule with 2 subdivisions to estimate...
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This note was uploaded on 05/12/2010 for the course CHEM 3A taught by Professor Fretchet during the Fall '08 term at Berkeley.

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Math16B - Spring 08 Final Review - Math 16B Final Review 1...

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