This preview shows pages 1–9. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Outline Continuity at a point Continuity on intervals and domains Exercises Math 1205 2.6 Continuity Heath David Hart Fall 2007 Heath David Hart Math 1205 2.6 Continuity Outline Continuity at a point Continuity on intervals and domains Exercises Table of Contents: Notes for Day 7: 2.6: Continuity Continuity at a point Onesided continuity Twosided continuity Continuity at a point Continuity on intervals and domains The Intermediate Value Theorem Exercises Heath David Hart Math 1205 2.6 Continuity Outline Continuity at a point Continuity on intervals and domains Exercises Review Last time, we discussed the three types of asymptotes: I Horizontal asymptotes I Vertical asymptotes I Oblique (slant) asymptotes Heath David Hart Math 1205 2.6 Continuity Outline Continuity at a point Continuity on intervals and domains Exercises Outline Today well cover three types of continuity : I Continuity at a point I Continuity over an interval I Continuity over a domain In addition, well cover the Intermediate Value Theorem , which well use in solving a problem in this weeks Mathematica Lab. Heath David Hart Math 1205 2.6 Continuity Outline Continuity at a point Continuity on intervals and domains Exercises Onesided continuity Twosided continuity Continuity at a point Continuity Continuity is a stronger, and more demanding, criterion for a function than limits. When we say that a function is continuous at some point, were saying not only that the limit of the function exists at that point, but more than that. Whereever a function is continuous, limits existbut not necessarily the other way around! Heath David Hart Math 1205 2.6 Continuity Outline Continuity at a point Continuity on intervals and domains Exercises Onesided continuity Twosided continuity Continuity at a point Onesided continuity at a point In the function shown here, the limit from the left as x approaches 3 exists: lim x 3 f ( x ) = 1 . Heath David Hart Math 1205 2.6 Continuity Outline Continuity at a point Continuity on intervals and domains Exercises Onesided continuity Twosided continuity Continuity at a point Onesided continuity at a point In fact, not only does the limit exist, but when x actually reaches 3, f (3) = 1 as well. We say that f ( x ) is continuous from the left at x = 1. Heath David Hart Math 1205 2.6 Continuity Outline Continuity at a point Continuity on intervals and domains Exercises Onesided continuity Twosided continuity Continuity at a point Onesided continuity at a point To be continuous from the left at a point x means that the limit from the left exists as x approaches x , but also that the function matches the limit at x ....
View
Full
Document
This note was uploaded on 03/31/2008 for the course MATH 1205 taught by Professor Fbhinkelmann during the Fall '08 term at Virginia Tech.
 Fall '08
 FBHinkelmann
 Calculus, Continuity

Click to edit the document details