1. AP CALCULUS 1004 Limits pt.3 Limits at Infinity and End Behavior

2. REVIEW: ALGEBRA is a ________________________ machine that ___________________ a function ___________ a point. CALCULUS is a ________________________ machine that ___________________________ a function ___________ a point

3. END BEHAVIOR

4. LIMITS AT INFINITY Part 2: End Behavior GENERAL IDEA: The behavior of a function as x gets very large ( in a positive or negative direction) ALREADY KNOW many functions: Polynomial: Trigonometric: Exponential: Logarithmic: NOW primarily RATIONAL and COMPOSITE.

5. END Behavior: Limit Layman’s Description: Notation: Horizontal Asymptotes: Note: m

6. GNAW: Graphing EX:

7. GNAW: Algebraic Method: DIRECT SUBSTITUTION gives a second INDETERMINANT FORM Theorem:

8. End Behavior Models EX: (with Theorem)

9. End Behavior Models Summary: ________________________________________ A). B). C).

10. Special Case Special Note: If the function involves an ABSOLUTE VALUE it may have TWO Horizontal Asymptotes. REM also: EX:

11. Review

12. Last Update: 08/09/10