Problem 1

(a). Consider the Plane . Find All Parallel Planes that Are a Distance 2 from the above Plane. Your Answer Should Be of the Form

(b). Find the Parametric Equation for the line of Intersection of the Planes and

(c). Find the Tangent Plane to at the point

Problem 2

A function at is known to have , , , and .

(a). A Bee Starts Flying at and Flies along the Unit Vector Pointing towards the point ) what is the Rate of Change of in This Direction?

(b). User a Linear Approximation of at the point to Approximate

(c). Let . a Bee Starts Flying at ; along Which Unit Vector Direction Should the Bee Fly such that the Rate of Change of and Are both Zero in This Direction

Problem 3

Let from some twice differentiable function .

(a). Find in terms of , , and

(b). Suppose . for what Constant Will

Problem 4

Find and classify all critical points of

The critical points and are saddle points, is a local maximum and is a local minimum

Problem 5

Consider the domain above the -axis and below the parabola in the -plane.

(a). Express as an Iterated Integral

(b). Compute the Integral in the case where

Problem 6

Let be the region inside the cylinder , below the plane and above the plane . Express the integral as three different iterated integrals corresponding to the orders of integration:

(a).