Tangent Planes and Normal Lines

1.         Find a unit normal vector to the surface at the indicated point:

 

2.         Find an equation of the tangent plane to the surface at the indicated point:

 

3.         Find the equation of the normal line to the surface at the indicated point:

 

4.         Show that any tangent plane to the cone z² = (ax)² + (by)² passes through the origin.

*5.       Suppose that f is any differentiable function of a single variable and suppose that a surface is defined by z = xf(y/x).  Show that the tangent plane at every point of this surface passes through the origin.