Section 14.3 Worksheet:

Assigned problems: Exercises pp. 889-890, #2, 4, 5, 9, 14, 16, 23, 34, 36 (due Monday, 12/1).

1. What is the curvature of a circle of radius r? What happens as r becomes small (approaches zero)? What happens as r becomes large (approaches )?

2. There are several planes defined by the unit tangent, normal, and binormal vectors: what is the significance of the plane containing
   • the tangent and normal, and
   • the normal and binormal?
   Which one osculates, and what does that mean?

3. Does a space curve define a unique vector-valued function? Or are there several vector-valued functions which may trace out the same space curve?

4. What is the advantage to parameterizing a curve by arc length?