Calculus 3 Timed Quiz 2

Definition (Unit Tangent and Unit Normal Vectors) If is a __________ function that defines a __________ graph, then at each point a __________  __________ vector is



and the principal unit __________ vector function is

Proposition (Arc Length Function) Let be a ______________   _____________  curve that is the graph of the vector function described parametrically by ,   and let be a particular point on (base point). Then the length of from the base point to the variable ____ is given by the arc length function

Proposition (Unit Tangent and Unit Normal Vectors) If has a piecewise smooth __________ and is represented as in terms of the arc length parameter , then the unit tangent vector and the principal unit normal vector satisfies



where is a scalar function of

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