1. Sect.1.5 continued Infinite Limits
Limits at infinity
Infinite limits

2. Consider the rational function
is undefined at x = 3
From the graph
And Table x
2.9
2.99
2.999 3
-68
-698
-6998 ?
3.0001
3.001
3.01
3.1 x ?
7002
702 72
Left:
Decreases without bound
Right:
Increases without bound

3. Now find the Limit graphically
NOTE: the function increases
or decreases without bound
NOTE: not the same
infinite limits do not exist

4. Limits and Notation
Limits at infinity
Infinite Limits

5. Find Is the denominator approaching 0- or 0+
Examining the behavior of the denominator
Test Point

6. Find
Is the denominator approaching 0- or 0+
Test Point

7. Infinite Properties
Let c and L be real numbers and let f and g be functions such that
L > 0
L < 0

8. 3) Find if and
Test point

9. 4) Find

10. Infinite Limits and Vertical Asymptotes
The line x = c is a vertical asymptote of if
and

11. 5) Find the vertical asymptote of
Set denominator equal to zero
Justify your answer
Right
Left
Test point
Since both limits tend to ± infinity,
the line x = 2 is a Vertical Asymptote

12. 6) Find the vertical asymptote of

13. 6) continued Right Left Test point
Since both limits tend to ±infinity, the line ,
where n is all integers, is a Vertical Asymptote

14. HOMEWORK Page 88 # 1 – 4, 13 – 23 odd, 29 – 32 all
# 37-43, 45, 47, 48, and 70
Work all problems analytically