13.2 Derivatives and Integrals of Vector Functions

13.2 Derivatives and Integrals of Vector Functions - Math...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 224 – Calculus III 1 13.2 Derivatives and Integrals of Vector Functions Recommended Homework: #1-39 Derivatives of Vector Functions Recall: From Calc I, 0 ( ) ( ) ( ) lim h f x h f x fx h slope of the tangent line to f at x What does () d t dt r r mean? Picture: x y z
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Math 224 – Calculus III 2 So, we can take derivatives component-wise. If ( ) ( ), ( ), ( ) t f t g t h t r then: ( ) ( ), ( ), ( ) d t f t g t h t dt r r Geometrically (and analogously to calc I derivatives) ( ) ( ), ( ), ( ) t f t g t h t r represents the tangent vector to the space curve ( ) ( ), ( ), ( ) t f t g t h t r . To find the tangent line to ( ) ( ), ( ), ( ) t f t g t h t r , we would find the equation of the line through the tangent point and parallel to the tangent vector () t r We denote the unit tangent vector by t r T r Example: Given the vector function 2 ( ) 1,5 2 t t t r and the value 1 t Sketch the curve for 03 t Find t r Sketch the position vector (1) r and the tangent vector r on the graph above.
Background image of page 2
Math 224 – Calculus III 3 Examples: Find the derivatives of the following vector functions: 12 ( ) tan ln( 1) t t t te t r i j k ( ) 2 tt r i j k ( )
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/31/2010 for the course MATH 224 taught by Professor Harris during the Fall '09 term at Illinois Central.

Page1 / 8

13.2 Derivatives and Integrals of Vector Functions - Math...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online