1.  Find the total differential of f(x,y) = cos(x^2 y) e^(y/x).

2.  Give the standard form equation for the plane tangent to the surface z(x,y) = x^(3/2) + 1 / sqrt(y) at the point (1, 4, 3/2).

3.  Find the direction from the point P = (1, 1, pi) in which the function f(x,y,z) = y cos( x^2 z ) decreases the most rapidly and compute the magnitude of the corresponding rate of change.

4.  Find the equation of all horizontal tangent planes to the surface 9 x^2 - 4 y^2 + 12 x - 25 y + z = 0.

5.  Use an incremental approximation to estimate the value of e^(-(x^2 + y^2)) at the point (x, y) = (.02, .01).

6.  Find the direction from the point P = (1/3, 3, 3) in which the function f(x,y,z) = z sqrt(x y) decreases the most rapidly and compute the magnitude of the greatest rate of change.

7.  Find a unit vector normal to the surface given by the equation 2 = x^2 + 2xy + 3y^2  - z at the point P = (1,1,4), and find the equation of the tangent plane at that point.

8.  Sketch and describe the traces of the quadric surface z = x^2/4 - y^2/25 with the xy, xz and yz planes.