Limits At Infinity 12.14.07

8

6

4

2

-2

-4

-6

-10 -5 5 10

Limits at Infinity(Horizontal Asymptotes)

... xAs

.0... y

.01

lim So,2x

x

2

1)(x

xf

3.5

3

2.5

2

1.5

1

0.5

-0.5

-1

-1.5

-2

-2.5

-4 -3 -2 -1 1 2 3 4 5

0lim rx x

c

3

1)(x

xf x

xf1

)(

The Golden Rule…

8

7

6

5

4

3

2

1

-1

-2 2 4 6 8 10 12

5

4

3

2

1

-1

-2

-3

-4

-6 -4 -2 2 4 6

xxf

1)(

xx

13lim

xxx

1lim3lim

10

8

6

4

2

-10 -5 5 10

3

03

42

1lim

x

xx

103

34lim

x

xx

2

72lim

2

x

xx

1

1lim

2

x

xx

042

33lim

3

2

x

xxx

2

3

42

33lim

2

2

x

xxx

exist!not ...does 42

33lim

3

4

x

xxx

Homework

p. 203 #9-18