Shelby Smith

A function is continuous if it is unbroken fro all values of x. T he formal definition states that f(x) is continuous if the limit as f(x) approaches a is equal to that of f(a).

It is also important to remember that the lim of f(a) exists iff f(x) approaching a from the left is equal to the lim f(x) as x approaches a from the right.

This can also be defined:

Therefore there are tree possible problems which cause discontinuity

I. f(a) is not defined

II. the limit _____may not exist

III. the limit____f(x) may exist but is not equal to f(a)

Sample Questions

1.http://www.richland.edu/james/lecture/m116/functions/piecewise1.gif

2. Suppose that f(x) is continuous at x=3 and that ____, which statements about f(x) must be true?

I. f(3)=17

II. 3 is in the domain of f(x)

III.______

3. Suppose that the function f(x) is continuous at x=2 and that f(x) is defined

_______

What is the value of a?

Answers

1.) 2.) All three 3.) 1/2

For more info:

http://64.233.169.104/search?q=cache:4gvwCaS-djIJ:community.middlebury.edu/~abbott/UA/UA-4-1.pdf+continuity+in+terms+of+limits&hl=en&ct=clnk&cd=5&gl=us

http://www.sasked.gov.sk.ca/docs/calc30/unit_c.htm

http://www.sparknotes.com/math/precalc/continuityandlimits/