Vector Valued Functions

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Presentation transcript:

Vector Valued Functions Section 11.1 Vector Valued Functions

Definition of Vector-Valued Function

How are vector valued functions traced out?

In practice it is often easier to rewrite the function. Sketch the curve represented by the vector-valued function and give the orientation of the curve. #26 r(t)= #34 r(t)=

Definition of the Limit of a Vector-Valued Function Do #72

Definition of Continuity of a Vector-Valued Function Do #78

Section 11.2 Differentiation and Integration of Vector-Valued Functions.

Definition of the Derivative of a Vector-Valued Function

Theorem 12.1 Differentiation of Vector-Valued Functions #12,

Theorem 12.2 Properties of the Derivative

Definition of Integration of Vector-Valued Functions #44, #54

Smooth Functions A vector valued function, r, is smooth on an open interval I if the derivatives of the components are continuous on I and r’ 0 for any value of t in the interval I. #30 Find the open interval(s) on which the curve is smooth.