This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 14 Vector Functions 14.1 Vector Functions and Space Curves Definition 14.1.1 Let r : R R 3 (or R 2 ) be given by r ( t ) = < f ( t ) ,g ( t ) ,h ( t ) > = f ( t ) i + g ( t ) j + h ( t ) k , where f , g , and h are real-valued functions. r ( t ) is called a vector-valued function. Definition 14.1.2 Let r ( t ) be given by r ( t ) = < f ( t ) ,g ( t ) ,h ( t ) > , where f , g and h are real-valued func- tions of t . The domain of r is the largest set of real numbers t so that r ( t ) is defined. Definition 14.1.3 Let r ( t ) be given by r ( t ) = < f ( t ) ,g ( t ) ,h ( t ) > , where f , g and h are real-valued func- tions of t . We say that the limit of r as t approaches a is the vector v if for any > , there is a number > so that whenever < | t- a | < then || r t- v || < . Theorem: Let r ( t ) = < f ( t ) ,g ( t ) ,h ( t ) > be a vector-valued function with real-valued component functions f , g , and h . If the component functions all have limits as t approaches a , i.e., lim...
View Full Document
This note was uploaded on 10/11/2010 for the course MTHSC 206 taught by Professor Chung during the Spring '07 term at Clemson.
- Spring '07
- Multivariable Calculus