mthsc206-fall-2010-notes-15.2

mthsc206-fall-2010-notes-15.2 - 15.2 Limits and Continuity...

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: 15.2 Limits and Continuity Recall: A real-valued function f of one variable has a limit L as x approaches the number a , i.e., lim x a f ( x ) = L , if there is an open interval containing a where f is defined (except possibly at x = a ), and if for every positive number there is a positive number so that whenever x is a number with < | x- a | < then | f ( x )- L | < . NOTE: The only way in which to approach the value a was along the x-axis from the left or from the right. So if lim x a- f ( x ) = lim x a + f ( x ) = L , then the two-sided limit existed and was equal to L . On the other hand, if the two one-sided limits didnt equal, we were able to conclude the two-sided limit didnt exist. How do these ideas change when f is a real-valued function of two or more variables? Definition 15.2.1 Let ( a, b ) be a point in the xy-plane and let r > . The open disk centered at ( a, b ) with radius r is denoted D r ( a, b ) and is given by D r ( a, b ) = { ( x, y ) | ( x- a ) 2 + ( y- b ) 2 < r } ....
View Full Document

This note was uploaded on 10/11/2010 for the course MTHSC 206 taught by Professor Chung during the Fall '07 term at Clemson.

Page1 / 3

mthsc206-fall-2010-notes-15.2 - 15.2 Limits and Continuity...

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