1. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Does not exist
number
number

2. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Does not exist
number
number

3. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Note:

4. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Example:
Example: 1
0.1 10
0.01
100
0.001
1000
------
-----
1,000,000 1
0.01 10
0.0001
100
1000
------
-----
10^(-12)
1,000,000

5. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs

6. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Limits at Infinity of Rational Functions
To evaluate the limit at infinity of any rational function, we first divide both the
numerator and denominator by the highest power of that occurs in the denominator.
Example:
Example:

7. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Remark:
To evaluate the limit at infinity of any rational function, we first divide both the
numerator and denominator by the highest power of that occurs in the denominator.
Example:
Example:
Example:
Remark:

8. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Notes:
Notes:

9. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Example:
Example:
Example:
Example:

10. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Notes:
Notes:

11. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Exam-1 Term-151

12. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Example: (ex80p116)
Multiply by conjugate radical.
Example:
Example:

13. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs

14. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Horizontal Asymptote &
The line
Is a horizontal asymptote

15. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Example:
The line
Is a horizontal asymptote

16. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Example:

17. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
EXAM-1 TERM-121

18. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphsb

19. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
To evaluate the limit at infinity of any rational function, we first divide both the
numerator and denominator by the highest power of that occurs in the denominator.
Multiply by conjugate radical.
Factor then take the limit

20. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Example:

21. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Example:
Example:

22. Postpone to sec2.6: Limits at Infinity:
Sec 2.2: Limit of Function and Limit Laws
Sec 2.3: CALCULATING LIMITS USING THE LIMIT LAWS
Postpone to sec2.6: Limits at Infinity:
Limit from one side does not exist
Find an example for a function such that the limit from right does not exist

23. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Example:
Example:

24. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs

25. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Vertical Asymptote
Horizontal Asymptote

26. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Who is going faster to infinity
Example:

27. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Example: Sketch the graph of

28. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs

29. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Factor then take the limit
Sandwich thm
high pwr in denomi
Rational func
Containing radicals
Remove the | |
Containing absolute value
Multiply by conjugate radical.
Containing noninteger
Use
Use graph
Use

31. Sec 2.6: Limits Involving Infinity; Asymptotes of Graphs
Reminder:
After sec2.5 continuity