chapter2

MATH NOTES: CHAPTER 2


Section 2.1: Algebraic and Numerical Limits

Definition of a limit: 
	assume f is defined in a neigborhood of c and let c and L be real numbers. The function f has limit L as x 	approaches c if, given any positive number ε, there is a positive number δ such that for all x,

	0 < |x-c| < δ →|f(x)-L|<ε 
	
The value of the function does not have to exist for the limit to exist.
The limit is the value that the function approaches, not what it is.

Could find by 
1. factoring
2. multiplying by conjugate
3. using logarithms
4. plugging in the x value of the limit

If one method doesn't work, try another!

Limits could be a point, or even infinity. When the value approached by both sides, what does y approach? That is the limit.

0/0 is an indeterminant form.

Appendix 3

Formal definition of a limit: limx→c (f(x))=L

ε is units from the limit
δ is interval of x values you can stay within to stay within ε units of the limit

if |x-L|<δ then |f(x)-L|<ε

use the smallest of the delta(δ)