Limits Cheat Sheet

Limits Cheat Sheet - © 2005 paul dawkins limits definitions precise definition : The limit exists, and we found it! What happens when we use direct substitution? The limit of f(x) as x approaches a: Web we can make f(x) as close to l as we want by taking x sufficiently close to a (on either side of a) without letting x = a. Same definition as the limit except it requires x > a. We say lim ( ) xa f x l → = if for every ε>0 there is a δ>0such that whenever 0<−<xa δ then f x l( )−< ε. The limit doesn't exist (probably an asymptote). The limit doesn't exist (probably an asymptote). The limit exists, and we found it!

The Limit Doesn't Exist (Probably An Asymptote).

Same definition as the limit except it requires x > a. G ( x) = x − 3 x + 5 − 3. The limit of f(x) as x approaches a: The limit exists, and we found it!

There Is A Similar Definition For Lim F(X) = L.

We say lim ( ) xa f x l → = The limit exists, and we found it! We say lim ( ) xa f x l → = if for every ε>0 there is a δ>0such that whenever 0<−

We Want To Find Lim X → 4 G ( X).

© 2005 paul dawkins limits definitions precise definition : The limit doesn't exist (probably an asymptote). Except we require x large and negative. The value to which the output (dependent variable) of f(x) approaches as x (independent variable) approaches the number a.

What Happens When We Use Direct Substitution?