aq1 - ,-2). Q2]. .. Compute the rst and second order...

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PRINT NAME: SOLUTIONS Calculus IV [2443–002] Quiz I Q1]. .. Which one of the four functions listed below has the following level curves? 1. f ( x,y ) = ( x + 1)( y - 2). NO – Level curves are hyperbolae with asymptotes parallel to the axes, and centered on ( - 1 , 2). 2. g ( x,y ) = ( x - 1)( y + 2). NO – Level curves are hyperbolae with asymptotes parallel to the axes, and centered on (1 , - 2). 3. h ( x,y ) = ( x + 1) 2 - ( y - 2) 2 . NO – Level curves are hyperbolae with asymptotes parallel to y = ± x , and centered on ( - 1 , 2). 4. k ( x,y ) = ( x - 1) 2 - ( y + 2) 2 . YES – Level curves are hyperbolae with asymptotes parallel to y = ± x , and centered on (1
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Unformatted text preview: ,-2). Q2]. .. Compute the rst and second order partial derivatives for the function f ( x,y ) = cos( xy ) . Answer: There are two rst order partial derivatives and four second order partial derivatives. The mixed second order partial derivatives are equal by Clairauts Theorem, so we get a total of ve answers. f x ( x,y ) =-y sin( xy ) f y ( x,y ) =-x sin( xy ) f xx ( x,y ) =-y 2 cos( xy ) f xy ( x,y ) = f yx ( x,y ) =-sin( xy )-xy cos( xy ) f yy ( x,y ) =-x 2 cos( xy )...
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This note was uploaded on 01/12/2010 for the course MATH 241 taught by Professor Teleman,c during the Winter '08 term at University of California, Berkeley.

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