mthsc206-fall-2010-notes-14.1

mthsc206-fall-2010-notes-14.1 - 14 Vector Functions 14.1...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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.

Ask a homework question - tutors are online