1. Vector Valued Functions
Section 11.1
Vector Valued Functions

2. Definition of Vector-Valued Function

3. How are vector valued functions traced out?

4. 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.
# r(t)=
# r(t)=

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

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

7. Section 11.2
Differentiation and Integration of Vector-Valued Functions.

8. Definition of the Derivative of a Vector-Valued Function

9. Theorem 12.1 Differentiation of Vector-Valued Functions
#12,

10. Theorem 12.2 Properties of the Derivative

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

12. 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’ for any value of t in the interval I.
#30 Find the open interval(s) on which the curve is smooth.