1205-hwt0206-slides

1205-hwt0206-slides - Outline Continuity at a point...

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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 One-sided continuity Two-sided 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 One-sided continuity Two-sided 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 One-sided continuity Two-sided continuity Continuity at a point One-sided 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 One-sided continuity Two-sided continuity Continuity at a point One-sided 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 One-sided continuity Two-sided continuity Continuity at a point One-sided 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 ....
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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.

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1205-hwt0206-slides - Outline Continuity at a point...

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