Exercises

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 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 when w is and h is , approximate the deflection when and .