Lesson 2-1: Rates of change and Limits Day #2 AP Calculus Mrs. Mongold

One-sided and Two-sided Limits When the values of a function f tend to be different limits as x approaches a number c from opposite sides we call the limit a two-sided limit. When x approaches c from the right it is called a right hand limit When x approaches c from the left it is called a left hand limit Right Hand: Left Hand:

Theorem A function f(x) has a limit as x approaches c if and only if the RHL and LHL at c are equal

Example 1

Example 2

Example 3 Find the limit at x=0 x=1 x=2 x=3 x=4

Greatest integer function

Sandwich Theorem (a.k.a. Squeeze Theorem) Use this when the limit cannot be found directly If g(x) < f(x) < h(x) for all x≠c in some interval about x, and

Example

Example

Homework Pg 62-63/ 1-6 all and 31 and 32