1. Warm-Up- Books and calcs
If f is continuous on [2, 6], with f (2) = 20 and f (6) = 10, then the Intermediate Value Theorem says which of the following is true?
I f (x) = 25 does not have a solution on [2, 6].
II f (x) = 17 has a solution on [2, 6].
III f (x) = 0 has a solution on [2, 6].
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III

2. 1-5: Infinite Limits Objectives:
Study functions with unbounded behavior (infinite limits)
Study relationship of infinite limits & vertical asymptotes
©2002 Roy L. Gover (

3. Definition
A function has an infinite limit at c if f(c) as xc. f(x) is unbounded at x=c.
f(x)
x=c

4. Important Idea
The idea of an infinite limit suggests that infinity has a value; this is not correct.
means the limit doesn’t exist at x=c.

5. Example
What is the limit as x1 from the left and from the right?
x=1

6. Try This
What is the limit as x1 from the left and from the right?
x=1

7. Try This
What is the limit as x1 from the left and from the right?
x=1

8. Definition
The value(s) that make the denominator of a rational function zero is a vertical asymptote.

9. Important Idea
As a function, it gets ever closer to the vertical asymptote

10. Example Determine all vertical asymptotes of Steps:
2. Set denominator to 0 & solve
1. Factor & cancel if possible

11. Example Find the limit if it exists: The questions…
1. When you substitute x=1, do you get a number/0 or 0/0?
2. What is happening at x= a value larger than 1?

12. Try This
Find the limit if it exists: +

13. Properties of Infinite LimitsIf
& 1.

14. Properties of Infinite LimitsIf
& 2.
if L>0

15. Properties of Infinite LimitsIf
& 3.
if L<0

16. Properties of Infinite LimitsIf
& 4.

17. Lesson Close
Infinite limits (unbounded behavior) is an important idea in the study of Calculus.

18. Assignment
88/1-13 odd,29-41 odd, 49