Problem 1

Let , , and

(a). The line Which Contains and is Perpendicular to the Triangle Has what Parametric Equations

(b). The Set of All Points such that is Perpendicular to Form what Geometry in Space Which Satisfy what Equation

The set of points forms a sphere of radius 1 centred at .

(c). If a light Source at the Origin Shines on the Triangle Making a Shadow on the Plane , then what is

Problem 2

Consider the function and . You are standing at the point .

(a). If You Jump from to the point then the Amount by Which Changes is what Approximately

(b). If You Jump from in the Direction along with Increases Most Rapidly, then Will Increase or Decrease

will increase.

(c). You Jump from in a Direction along Which the Rate of Change of and Are both 0 an Example of such a Direction is what

Problem 3

Suppose is twice differentiable (with ), and and .

(a). Determine , , and in terms of Functions Depending on and/or , and Partial Derivatives with respect to and/or