4B Limits at Infinity

1

Limits At Infinity, Infinite Limits

4B Limits at Infinity

2

Definition: (Limit as )

We say that if for every there is a corresponding number, such that

is defined on for

m

c ∈ ℜ

then

4B Limits at Infinity

3

EX 1 Intuitively (looking at the graph) determine these limits.

EX 2 Show that if n is a positive integer, then .

4B Limits at Infinity

4

EX 3

EX 4

EX 5

4B Limits at Infinity

5

Definition: (Infinite limit )

We say if for every positive number, m

there is a corresponding δ > 0 such that

4B Limits at Infinity

6

EX 6 Determine these limits looking at this graph of .

Ex 7 Find the horizontal and vertical asymptotes for this function,

then write a few limit statements including ∞.

4B Limits at Infinity

7

Ex 8 a) Find the vertical and horizontal asymptotes for this function.

b) Determine these limits:

4B Limits at Infinity

8

Determine these limits: