1. Chapter 12 Vector-Valued Functions

2. Copyright © Houghton Mifflin Company. All rights reserved.12-2 Definition of Vector-Valued Function

3. Copyright © Houghton Mifflin Company. All rights reserved.12-3 Figure 12.1

4. Copyright © Houghton Mifflin Company. All rights reserved.12-4 Definition of the Limit of a Vector-Valued Function

5. Copyright © Houghton Mifflin Company. All rights reserved.12-5 Figure 12.6

6. Copyright © Houghton Mifflin Company. All rights reserved.12-6 Definition of Continuity of a Vector-Valued Function

7. Copyright © Houghton Mifflin Company. All rights reserved.12-7 Definition of the Derivative of a Vector-Valued Function

8. Copyright © Houghton Mifflin Company. All rights reserved.12-8 Figure 12.8

9. Copyright © Houghton Mifflin Company. All rights reserved.12-9 Theorem 12.1 Differentiation of Vector-Valued Functions

10. Copyright © Houghton Mifflin Company. All rights reserved.12-10 Theorem 12.2 Properties of the Derivative

11. Copyright © Houghton Mifflin Company. All rights reserved.12-11 Definition of Integration of Vector-Valued Functions

12. Copyright © Houghton Mifflin Company. All rights reserved.12-12 Figure 12.10

13. Copyright © Houghton Mifflin Company. All rights reserved.12-13 Definitions of Velocity and Acceleration

14. Copyright © Houghton Mifflin Company. All rights reserved.12-14 Figure 12.16

15. Copyright © Houghton Mifflin Company. All rights reserved.12-15 Theorem 12.3 Position Function for a Projectile

16. Copyright © Houghton Mifflin Company. All rights reserved.12-16 Definition of Unit Tangent Vector

17. Copyright © Houghton Mifflin Company. All rights reserved.12-17 Definition of Principal Unit Normal Vector

18. Copyright © Houghton Mifflin Company. All rights reserved.12-18 Figure 12.22

19. Copyright © Houghton Mifflin Company. All rights reserved.12-19 Theorem 12.4 Acceleration Vector

20. Copyright © Houghton Mifflin Company. All rights reserved.12-20 Theorem 12.5 Tangential and Normal Components of Acceleration

21. Copyright © Houghton Mifflin Company. All rights reserved.12-21 Figure 12.24

22. Copyright © Houghton Mifflin Company. All rights reserved.12-22 Theorem 12.6 Arc Length of a Space Curve

23. Copyright © Houghton Mifflin Company. All rights reserved.12-23 Definition of Arc Length Function and Figure 12.29

24. Copyright © Houghton Mifflin Company. All rights reserved.12-24 Theorem 12.7 Arc Length Parameter

25. Copyright © Houghton Mifflin Company. All rights reserved.12-25 Figure 12.31

26. Copyright © Houghton Mifflin Company. All rights reserved.12-26 Figure 12.32

27. Copyright © Houghton Mifflin Company. All rights reserved.12-27 Definition of Curvature

28. Copyright © Houghton Mifflin Company. All rights reserved.12-28 Theorem 12.8 Formulas for Curvature

29. Copyright © Houghton Mifflin Company. All rights reserved.12-29 Figure 12.34

30. Copyright © Houghton Mifflin Company. All rights reserved.12-30 Theorem 12.9 Curvature in Rectangular Coordinates

31. Copyright © Houghton Mifflin Company. All rights reserved.12-31 Figure 12.35

32. Copyright © Houghton Mifflin Company. All rights reserved.12-32 Figure 12.37

33. Copyright © Houghton Mifflin Company. All rights reserved.12-33 Theorem 12.10 Acceleration, Speed, and Curvature

34. Copyright © Houghton Mifflin Company. All rights reserved.12-34 Figure 12.38

35. Copyright © Houghton Mifflin Company. All rights reserved.12-35 Summary of Velocity, Acceleration, and Curvature