1. 3.5
Limits at Infinity
If r is a positive rational number and c is any real
number, then
Furthermore, if xr is defined when x < 0, then
(Horizontal asymptote at y = 0)

2. Ex. 1
Degree of Num. =
Degree of Den. or
Divide by the highest
degree of the denominator.
Ex. 2
= 2

3. The highest degree in all 3 is an x2
Ex. 3
The highest degree in all 3 is an x2 a. 3 2 b. 3 c.
limit D.N.E. when
deg of N > deg of den 3

4. Ex. 4
a. For x > 0
b. For x < 0

5. Ex. 5 1 -1
The sin x function oscillates between –1 and 1,
therefore the limit D.N.E..

6. The Squeeze Theorem
since
Ex. 6
find the limit by dividing each
term by x.
since the