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  1. Consider the function


    and let P be the point (2,3,5).

    1. At the point P, find the direction (vector) where f has the maximum descend.
    2. Find the equation of the tangent plane to the surface f(x,y,z) = 3 at the point P.
    3. Approximate the value of f(1.98,3.03,4.97) using the method of differentials.
  2. A horizontal beam is supported at both ends and supports a uniform load. The deflection at its midpoint is given by tex2html_wrap_inline205 where w and h are the width and height of the beam, repectively, and k is a constant that depends on the composition of the beam and the amount of the load. Suppose S is tex2html_wrap_inline215 when w is tex2html_wrap_inline219 and h is tex2html_wrap_inline223 , approximate the deflection when tex2html_wrap_inline225 and tex2html_wrap_inline227 .

Sean O Anderson
Tue Apr 15 11:51:21 EDT 1997