lect11_2

lect11_2 - Calculus of Vector-Valued Functions(11.2 1...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

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

Unformatted text preview: Calculus of Vector-Valued Functions - (11.2) 1. Limits: Let r ! ! t " "# f ! t " , g ! t " , h ! t " $ be a vector-valued function. Then lim t % a r ! ! t " " lim t % a # f ! t " , g ! t " , h ! t " $"# lim t % a f ! t " , lim t % a g ! t " , lim t % a h ! t " $ provided lim t % a f ! t " lim t % a g ! t " lim t % a h ! t " all exist. If one of the limits does not exists, then lim t % a r ! ! t " does not exist. Example Find the limit if it exists. a . lim t % # 1 t 2 & 1 , tant , ln ! t & 1 " $ b . lim t % ! # 1 " 2 t 2 3 t 2 & t , te " 2 t , sin ! ! t " $ c . lim t " # sint t , t lnt , 1 t " 1 $ a. lim t % # 1 t 2 & 1 , tan t , ln ! t & 1 " $"# t , 0, 0 $ b. lim t % ! # 1 " 2 t 2 3 t 2 & t , te " 2 t , sin ! ! t " $"# " 2 3 , 0, DNE $ , so the limit does not exist. c. lim t " # sin t t , t ln t , 1 t " 1 $"# 1, "! " 0, " 1 $"# 1,0, " 1 $ 2. Continuity The vector-valued function r ! ! t " "# f ! t " , g ! t " , h ! t " $ is continuous at t " a whenever lim t % a r ! ! t " " r ! ! a " . So r ! ! t " is continuous at t " a if and only if lim t % a f ! t " " f ! a " lim t % a g ! t " " g ! a " lim t % a h ! t " " h ! a " . Again if one them is not continuous at t " a , r ! ! t " is not continuous at t " a . Example Determine for what values of t the vector-valued function r " ! t " "# tant , ln ! t & 1 " , 1 " t $ is continuous. f ! t " " tan ! t " , D f " t : " 3 ! 2 , " ! 2 , " !...
View Full Document

This note was uploaded on 02/05/2012 for the course MATH 2142 taught by Professor Lerna during the Fall '10 term at FIU.

Page1 / 6

lect11_2 - Calculus of Vector-Valued Functions(11.2 1...

This preview shows document pages 1 - 2. Sign up to view the full document.

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