Warm-Up Draw and complete a unit circle from memory First – try to complete as much as possible on your own (no neighbors!) First – try to complete as much as possible on your own (no neighbors!) Second – ask a neighbor for a hint (not the whole thing) Second – ask a neighbor for a hint (not the whole thing)

Section 2.2 The Limit of a Function SWBAT: Define a limit Find limits and Graphically

What is a limit?

3 examples where the limit still exists

General Definition The y-value that you get closer to as you approach some given x-value. This is read, “the limit of f of x, as x approaches a, is L” (L is some y-value)

One-Sided Limits Sometimes a function f(x) approaches two different limits as x approaches a number a from the left or from the right. This leads to the following definition: Limit of f(x) as x approaches a from the left is equal to L.

One-Sided Limits (cont’d) We similarly define right-hand limit. Both definitions are illustrated below:

One-Sided Limits (cont’d) The relationship between limits and one- sided limits is given by the following: In other words, “ for a limit to exist: the right hand limit and the left hand limit must equal each other.”

One-Sided Limits (cont’d) (g) g(0) (h) g(2) (i) g(5)

Assignment 6 p