1. 1 Limits at Infinity Section 3.5

2. 2 Horizontal Asymptotes The line y = L is a horizontal asymptote of the graph of f if

3. 3 Example Check out TABLE on calculator.

4. 4 Limits at Infinity If r is a positive rational number and c is any real number c, then. Furthermore, if x r is defined for x < 0, then.

5. 5 Examples Strategy: Divide each term of the numerator and denominator by the highest power of x in the denominator.

6. 6 Examples

7. 7

8. 8 Limits at Infinity Guidelines for finding limits at infinity of rational functions If degree of numerator is less than degree of denominator, the limit is zero. If degree of numerator is equal to degree of denominator, the limit is the ratio of the leading coefficients. If degree of numerator is greater than degree of denominator, the limit does not exist.

9. 9 End Behavior End behavior of the graph of functions: What does graph do as ? Example: Describe end behavior of

10. 10 End Behavior Example: Describe end behavior of

11. 11 Homework Section 3.5 page 205 #1, 3-8 all, 17, 21-25 odd, Full curve sketches for 55, 59, 65, 67