1. In symbol, we write this as
LIMIT AT INFINITY
Consider the function
Investigate the behavior of f(x) as x decreases
without bound x -1 -5
-10
-100
-1000
-10,000
f(x) 1
1.92
1.98
1.9998
In symbol, we write this as

2. In symbol, we write this as
Consider the function
Investigate the behavior of f(x) as x increases
without bound x 1 5 10
100
1000
10,000
f(x)
1.92
1.98
1.9998
In symbol, we write this as

3. horizontal asymptote

4. Theorem : Let n be a positive integer, then

8. Horizontal asymptote

9. x = -2 (vertical asymptote) y = 2 is a horizontal asymptote
Dh: all x R except x = -2
When x = 0 , y = - 3 (y – int)
When y = 0 , x = 3 (x – int)
x = -2 (vertical asymptote)
y = 2 is a horizontal asymptote x
- 4
- 3
- 1
y = h(x) 7 12
- 8 9

10. x = -2 (vertical asymptote) y = 2 is a horizontal asymptote
Dh: all x R except x = -2
horizontal asymptote
y = 2
x = -2 (vertical asymptote) x
- 4
- 3
- 1
y = h(x) 7 12
- 8
(0, -3) , (3, 0)
vertical asymptote
x = -2
y = 2 is a horizontal asymptote 10

11. Df: all x R except x = -2 & x = 2
When x = 0 , (y – int)
When y = 0 , x = -1 (x – int)
x = -2 (vertical asymptote)
x = 2 (vertical asymptote) x -4 -3
-1.5 1 3 4
f(x)
(-1/4)
(-2/5)
(2/7)
(-2/3)
(4/5)
(5/12)
-0.25
-0.4
0.286
-0.67
0.8
0.417
y = 0
(horizontal asymptote) 11

12. Df: all x R except x = -2 & x = 2
x = -2 (vertical asymptote)
vertical asymptote
horizontal asymptote
x = -2
y = 0
x = 2 (vertical asymptote)
x = 2
vertical asymptote
y = 0 (horizontal asymptote) x -4 -3
-1.5 1 3 4
f(x)
(-1/4)
(-2/5)
(2/7)
(-2/3)
(4/5)
(5/12)
-0.25
-0.4
0.286
-0.67
0.8
0.417 12

15. x -1 1 f (x) e EVALUATING LIMITS OF EXPONENTIAL FUNCTIONS Using graph1
f (x) e
Using graph
(1 , e)
(0 , 1) 15

16. 16

17. EVALUATING LIMITS OF Logarithmic FUNCTIONS
Using graph

18. EVALUATING LIMITS OF Logarithmic FUNCTIONS
Using graph

19. EVALUATING LIMITS OF Trigonometric FUNCTIONS
Using graph

20. EVALUATING LIMITS OF Trigonometric FUNCTIONS
Using graph

22. EVALUATING LIMITS OF SPECIAL FUNCTIONS
Using graph

23. EVALUATING LIMITS OF SPECIAL FUNCTIONS
Using graph

24. EVALUATING LIMITS OF SPECIAL FUNCTIONS
Using graph