1205-hwt0203-slides

1205-hwt0203-slides - Outline Error tolerance Complementary...

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Unformatted text preview: Outline Error tolerance Complementary Tolerance The Definition of a Limit Math 1205 § 2.3: Epsilon-Delta Definition Heath David Hart Fall 2007 Heath David Hart Math 1205 § 2.3: Epsilon-Delta Definition Outline Error tolerance Complementary Tolerance The Definition of a Limit Review Goals Table of Contents: Notes for Day 3: § 2.3: Epsilon-Delta Definition Review Goals Error tolerance Complementary Tolerance Example 4 Exercise 25 The Definition of a Limit The “Plain English” Definition Example 2 Exercise 43* The “Mathematical Jargon” Definition Heath David Hart Math 1205 § 2.3: Epsilon-Delta Definition Outline Error tolerance Complementary Tolerance The Definition of a Limit Review Goals Review Last time, we discussed algebraic methods for finding limits: I The “limit-friendly” functions I The problem functions: I Fractions I Even-numbered roots I Logarithms I Piecewise-defined functions I Cancellation of common terms in fractions I Multiplying by the conjugate to eliminate roots Heath David Hart Math 1205 § 2.3: Epsilon-Delta Definition Outline Error tolerance Complementary Tolerance The Definition of a Limit Review Goals Goals Today, we’ll give a precise mathematical meaning of the concepts of “close to” and “approaches” that we’ve been using informally so far. Heath David Hart Math 1205 § 2.3: Epsilon-Delta Definition Outline Error tolerance Complementary Tolerance The Definition of a Limit Error tolerance Suppose x takes on a certain value that is not exactly equal to x , but lies inside an interval I containing x . The error tolerance is the largest two-sided margin of error around x which does not go outside the interval I . Heath David Hart Math 1205 § 2.3: Epsilon-Delta Definition Outline Error tolerance Complementary Tolerance The Definition of a Limit Error tolerance For example, suppose that x is approaching the value x = 5, and lies somewhere within the interval (4 , 7): Heath David Hart Math 1205 § 2.3: Epsilon-Delta Definition Outline Error tolerance Complementary Tolerance The Definition of a Limit Error tolerance This interval allows for a margin of error of 1 unit on the left side of x = 5, and a margin of error of 2 units on the right side. However, 1 unit is the largest margin of error which works on both sides , so the error tolerance is 1 unit. Heath David Hart Math 1205 § 2.3: Epsilon-Delta Definition Outline Error tolerance Complementary Tolerance The Definition of a Limit Error tolerance Here’s another example: x = 6, and x is approaching x with allowed values in the interval (2 , 8). What is the error tolerance? Heath David Hart Math 1205 § 2.3: Epsilon-Delta Definition Outline Error tolerance Complementary Tolerance The Definition of a Limit Error tolerance If x =- 1, and the error tolerance is 0 . 3, what interval represents how close x must be to 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-hwt0203-slides - Outline Error tolerance Complementary...

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