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

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

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:

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.

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.

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.

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.

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

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…

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