This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 2224 Multivariable Calc Sec. 12.2: Limits and Continuity in Higher Dimensions I. Review from math 1205 A. Limits 1. Def n : Let f be a fn defined on some open interval that contains the number a , except possibly at a itself. Then we say that the limit of f(x) as x approaches a is L , and we write lim x ! a f x ( ) = L if for every number >0 there is a corresponding number >0 such that  f(x)L < whenever 0< xa < Another way of writing the last line of this def n is: if 0< xa < then  f(x)L < 2. Th m : lim x ! a f x ( ) =L iff lim x ! a f x ( ) = lim x ! a + f x ( ) =L, where a , L are real numbers. 3. Some of the Limit laws Let f and g be any 2 functions st lim x ! a f x ( ) = L and lim x ! a g x ( ) = M and suppose that c is a constant. Then a. Sum/Difference Rule: lim x ! a f x ( ) g x ( ) " # $ % = lim x ! a f x ( ) lim x ! a g x ( ) = L M b. Constant Multiple: lim x ! a c f x ( ) " # $ % = c lim x ! a f x ( ) = cL c. Product Rule:...
View
Full
Document
This note was uploaded on 04/05/2008 for the course MATH 2224 taught by Professor Mecothren during the Spring '03 term at Virginia Tech.
 Spring '03
 MECothren
 Multivariable Calculus, Limits

Click to edit the document details