Chapter 13 VectorValued Functions and Motion in Space

  • Slides: 73
Download presentation
Chapter 13 Vector-Valued Functions and Motion in Space Thomas' Calculus: Early Transcendentals, 14 e

Chapter 13 Vector-Valued Functions and Motion in Space Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 1 of 75

Section 13. 1 Curves in Space and Their Tangents Thomas' Calculus: Early Transcendentals, 14

Section 13. 1 Curves in Space and Their Tangents Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 2 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 3 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 4 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 5 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 6 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 7 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 8 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 9 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 10 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 11 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 12 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 13 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 14 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 15 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 16 of 75

13. 2 Integrals of Vector Functions; Projectile Motion Thomas' Calculus: Early Transcendentals, 14 e

13. 2 Integrals of Vector Functions; Projectile Motion Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 17 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 18 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 19 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 20 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 21 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 22 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 23 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 24 of 75

Section 13. 3 Arc Length in Space Thomas' Calculus: Early Transcendentals, 14 e Copyright

Section 13. 3 Arc Length in Space Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 25 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 26 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 27 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 28 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 29 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 30 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 31 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 32 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 33 of 75

Section 13. 4 Curvature and Normal Vectors of a Curve Thomas' Calculus: Early Transcendentals,

Section 13. 4 Curvature and Normal Vectors of a Curve Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 34 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 35 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 36 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 37 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 38 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 39 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 40 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 41 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 42 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 43 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 44 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 45 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 46 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 47 of 75

Section 13. 5 Tangential and Normal Components of Acceleration Thomas' Calculus: Early Transcendentals, 14

Section 13. 5 Tangential and Normal Components of Acceleration Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 48 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 49 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 50 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 51 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 52 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 53 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 54 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 55 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 56 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 57 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 58 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 59 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 60 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 61 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 62 of 75

Section 13. 6 Velocity and Acceleration in Polar Coordinates Thomas' Calculus: Early Transcendentals, 14

Section 13. 6 Velocity and Acceleration in Polar Coordinates Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 63 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 64 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 65 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 66 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 67 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 68 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 69 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 70 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 71 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 72 of 75

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc.

Thomas' Calculus: Early Transcendentals, 14 e Copyright © 2018, 2014, 2010 Pearson Education Inc. Slide 73 of 75