Do Now: 1.Complete the table: 2.Why do you suppose you weren’t asked to evaluate f(4)? 3.Describe the behavior of the values in the f(x) column as the values in the x column get close to 4.

Have you reached your limit? an introduction to limits and evaluating limits

A limit problem asks, as x approaches some value, what does f(x) approach? Read “the limit as x approaches a of f(x) is what?”

In a later lesson, you are going to learn some methods of evaluating limits. For the time being, you will use t-tables to help you evaluate limits. You were actually evaluating a limit in the “do now” activity:

The table feature of a graphing utility is useful in evaluating limits. Calculator instructions: Go to the Y= screen and type in the function. Use 2 nd WINDOW (TBL SET) to set the start value at 3 and the step value (∆ Tbl) to Use 2 nd GRAPH to view the table.

Because polynomial functions are continuous and have all real numbers as their domain,

A limit problem does NOT ask what happens when you evaluate a function at some x value. It asks what is happening as x approaches some value. A limit can exist x→a even when f(a) does not exist. From the “do now” activity:

Limits can be evaluated from the left-hand, right-hand, or both directions: from the left: from the right:

Some limits do not exist. In order for a limit to exist, the limit as x approaches some value from the left must equal the limit as x approaches that same x value from the right.

DNE

If f(x) increases without bound (goes to infinity) or decreases without bound (goes to negative infinity), then the limit does not exist. DNE

Evaluate the limit: