12 2 Evaluating Limits Algebraically PRECALCULUS Objectives Evaluate

12. 2: Evaluating Limits Algebraically PRE-CALCULUS Objectives: • Evaluate limits of polynomial and rational functions at selected points. • Evaluate limits of polynomial and rational functions at infinity.

What you need to watch for: �What kind of functions have undefined values? �Otherwise, you can just plug in the value to find the limit!

Example 1 Use the properties of limits to evaluate. A. B.

� Limits of polynomial and rational functions can be found by direct substitution, as long as the denominator of the rational function evaluated is not 0.

Example 2 Use direct substitution, if possible to evaluate. If not possible explain why. A. B.

C. D.

Homework Answers �

Example 3 A. Evaluate . B. Evaluate

Example 4 A. Evaluate B. Evaluate

Warm-Up �

Example 5 A. Evaluate B. Evaluate

Example 5 C. Evaluate D. Evaluate

Example 6 A. Evaluate B. Evaluate

Horizontal Asymptotes/Limits

C. Evaluate

Example 7 A. Write the first five terms of the sequence . Then find the limit of the sequence, if it exists.

B. Write the first five terms of the sequence . Then find the limit of the sequence, if it exists.