Warm-Up
Draw and complete a unit circle from
memory


First – try to complete as much as possible on
your own (no neighbors!)
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
lim f  x   L
xa
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:
lim_ f  x   L
xa
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 onesided 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. 106 3-6