1. Calculus III 13.1 Vector-Valued Functions
Friday
September 23, 2016
Concordia College

2. Example 1: Airplane Flight Path, Vectors Indicating Position

3. Example 1: Airplane Flight Path, Vectors Indicating Position

4. Definition: Vector-Valued Function

5. Example 2

6. Example 2

7. Example 2

8. Example 3

9. Example 3

10. Example 4

11. Example 4

12. Example 5: Matching

13. Example 6 Intersection of Cone and Plane

14. Example 7
Parametrize the intersection of the plane 𝑦=1/2 with the sphere 𝑥 2 + 𝑦 2 + 𝑧 2 =1.

15. Example 7
Parametrize the intersection of the plane 𝑦=1/2 with the sphere 𝑥 2 + 𝑦 2 + 𝑧 2 =1.

16. Example 8
Describe the curve 𝐫 𝑡 =𝑡 sin 𝑡 𝐢+𝑡 cos 𝑡 𝐣+ 𝑡 2 𝐤 and its projections onto the xy-plane and the yz-plane. Find a circular paraboloid on which the curve lies.

17. Example 8

18. Example 9
Show that the graph of 𝐫 𝑡 =3 cos 𝑡 𝐢+3 sin 𝑡 𝐣+3 sin 𝑡 𝐤 Lies on both a circular cylinder and a plane. What shape is it? Find the length of the major and minor axes.

19. Example 9: Picture

20. 10. Particle Collision

21. 11. Limits

22. 12. Example

23. 13. Continuity

24. 14. Theorem on Continuity

25. 15. Example