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Unformatted text preview: r + s ) and z = sin( r + s ). 7. (a) Find the directional derivative of the function f ( x, y, z ) = x 3-xy 2-z at the point P(1,1,0) in the direction from Q(1,-1,1) to R(3,-2,7). (b) In what direction does of change most rapidly at P, and what are the rates of change in these directions. 8. Show that f ( x, y ) = e-x cos( y )-e-y cos( x ) satisﬁes Laplace’s Equation ∂ 2 f ( x, y ) ∂x 2 + f yy ( x, y ) = 0....
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This note was uploaded on 01/24/2011 for the course MATH 22 taught by Professor Brigham during the Winter '08 term at Missouri S&T.
- Winter '08