1. Finding Limits A Graphical & Numerical Approach
AP Calculus
August 29, 2016
Mrs. Agnew

2. Essential Question Essential Vocabulary
How do you find the limit of a function
graphically and numerically?
Essential Vocabulary
Limit
One-Sided Limit

3. An Introduction to Limits
Given f(x) = x2, describe the behavior of the function as x gets closer to 2.
It appears that as x approaches 2, the value of the function gets closer to 4.
Notation:

4. The Informal Definition of Limits
“The limit of f(x), as x approaches a, is L”
By selecting values for x sufficiently close to a (on both sides of a), but not equal to a, we get values of f(x) close to L.

5. Limit of f(x) ≠ Value of f(x)
Notice in the definition that we choose values of x close to a, BUT NOT EQUAL TO A.
The limit of a function has nothing to do with the value of the function at a.
The function does not even have to be defined at a for the limit to exist.
The limit of the function does not have to equal the value of the function at x = a.

6. Finding Limits Graphically
Investigating a limit graphically means to use the graph of the function to identify the limit.
Remember to look for what the y values approach, not the value of the function at x = a.

7. One Sided Limits
One sided limits have x → a either from the left OR the right.
Right Sided Limit Left Sided Limit
Consider ONLY
those numbers
BIGGER than a.
Consider ONLY
those numbers
SMALLER than a.

8. One-Sided Limits
The limit MUST be the same from the left and the right.
If not, the limit DNE (does not exist).
if and only if
and
Guided Practice

9. Finding Limits Numerically
To find a limit numerically means to choose values for x close to a on either side of a.
We will investigate what happens to the y values as x approaches a.
Use the table feature on your calculator.
Examples…

10. Homework: 8/29/16
Page 54 – 56
#4, 5, 7, 9, 17, 19, 25, 26,
28, 29, 31, 32, 71 – 74