11.4 Limits at Infinity

Lxfx

)(lim

“x gets infinitely large”

11.4 Limits at Infinity

Lxfx

)(lim

The line y = L is a Horizontal

Asymptote of f(x).

11.4 Limits at Infinity

degree of NUM = degree of DEN

Limit =

leading coefficient

leading coefficient

degree of NUM < degree of DEN

Limit = 0

11.4 Limits at Infinity

degree of NUM > degree of DEN.

Limit DNE because it increases infinitely.

11.4 Limits at Infinity

Ex 1: Evaluate

145

23lim

2

4

xx

xxx

Ex 2: Evaluate

2

17limxx

Ex 3: Evaluate

2

2

3

3

12lim

x

x

x

xx

11.4 Limits of Sequences

Lann

lim

11.4 Limits of Sequences

• If the limit exists, then an converges.

• If the limit DNE, then an diverges.

Ex 4: Write the first 4 terms and find the limit of the

sequence:

2

1

n

nnan

11.4 pg.817 # 9 – 27 odds,# 39 – 51 EOO