Precise def of a limit - The Precise Definition of a Limit...

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: The Precise Definition of a Limit We wish to give precise meanings to statements such as “ x is close to a ”, and to give a precise definition of lim x → a f ( x ) = L . The distance between two numbers a and b is given by | a- b | . For example, the distance between 4 and 7 is | 4- 7 | = 3. So to say two numbers x and a are close, we ask that | x- a | be small. We can say | x- 3 | < . 01 to say that x is within 0 . 01 of 3. We often use the Greek letters δ and ² (delta and epsilon) to denote small positive numbers. We might say “let δ > 0 and suppose | x- a | < δ ”, to say that x is to be close to a . We might say “let ² > 0 and suppose | f ( x )- L | < ² ”, to say that f ( x ) is close to L . Example. Consider lim x → 3 (4 x- 7) = 5. We ask the question: how close must x be to 3 for 4 x- 7 to be within 0 . 01 units of 5? For 4 x- 7 to be within 0 . 01 units of 5, we must have | (4 x- 7)- 5 | < . 01. We can solve this inequality. We have | 4 x- 7- 5 | < . 01 or | 4 x- 12 | < . 01 or | 4( x- 3) | < . 01. So 4 | x- 3 |...
View Full Document

This note was uploaded on 01/19/2009 for the course MAT 1214 taught by Professor Johnrayko during the Spring '08 term at The University of Texas at San Antonio- San Antonio.

Page1 / 2

Precise def of a limit - The Precise Definition of a Limit...

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