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)=

jttit 22 1kt

tjti2

sin4cos3

kt

tjti2

sin4cos3

Definition of the Limit of a Vector-Valued Function

Definition of Continuity of a Vector-Valued Function

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

Theorem 12.2 Properties of the Derivative

Definition of Integration of Vector-Valued Functions

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.

jir cos1sin)(