1. 1.5 Infinite Limits If
Then x = a is a VA of f (x).

2. If ,then it is an Indeterminant Limit.
1.5 Infinite Limits
If , then x = a is a VA.
If ,then it is an Indeterminant Limit.

3. Ex 1: Determine all Vertical Asymptotes

4. Ex 2: Evaluate

5. 1.5 pg. 88 #1 – 7 odds, #9 – 25 EOO, #29 – 47 odds

6. 3.5 Limits at Infinity If
Then y = L is a HA of f(x).

7. degree of NUM = degree of DEN
3.5 Limits at Infinity
degree of NUM = degree of DEN
Limit =

8. degree of NUM < degree of DEN
3.5 Limits at Infinity
degree of NUM < degree of DEN
Limit = 0

9. 3.5 Limits at Infinity degree of NUM > degree of DEN.
Limit DNE because it increases infinitely.

10. Ex 1: Evaluate

11. Ex 2: Identify the infinite limits, limits at infinity, & asymptotes
*see graph.

12. Ex 3: Find the VA’s & HA’s of f(x).

13. Ex 4: Evaluate

14. Ex 5: Evaluate

15. Ex 6: Sketch the graph by finding intercepts and limits:

16. 3.5 pg #3 – 8 all, #9, 13, 15, 17, 19, #21 – 33 EOO, #35, 37, 41, 45