1. 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. #26 r(t)= #34 r(t)=

5. Definition of the Limit of a Vector-Valued Function

6. Definition of Continuity of a Vector-Valued Function

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

10. Theorem 12.2 Properties of the Derivative

11. Definition of Integration of Vector-Valued Functions

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