Finding Limits A Graphical & Numerical Approach

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

2. Essential Question 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 SMALLER than a. Consider ONLY those numbers BIGGER 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