Continuity - Continuity We have seen that any polynomial...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Continuity We have seen that any polynomial function P ( x ) satisfies: for all real numbers a . This property is known as continuity . Definition. Let f ( x ) be a function defined on an interval around a . We say that f ( x ) is continuous at a iff Otherwise, we say that f ( x ) is discontinuous at a . Note that the continuity of f ( x ) at a means two things: (i) exists, (ii) and this limit is f ( a ). So to be discontinuous at a , means (i) does not exist, (ii) or if exists, then this limit is not equal to f ( a ). Basic properties of limits imply the following: Theorem. If f ( x ) and g ( x ) are continuous at a. Then (1) f ( x ) + g ( x ) is continuous at a ; (2)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
is continuous at a , where is an arbitrary number; (3) is continuous at a ; (4) is continuous at a , provided ; (5) If f ( x ) is positive, i.e. , then is continuous at a ; (6) If f ( x ) is continuous at a and g ( x ) is continuous at f ( a ), then their composition is continuous at a . Remark.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/26/2009 for the course CHE CHE 151 1A taught by Professor Koong during the Spring '09 term at Michigan State University.

Page1 / 5

Continuity - Continuity We have seen that any polynomial...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online