1. 2.7 Limits involving infinity Wed Sept 16
Do Now
Find

2. Determining the sign of infinity
To determine whether it is positive or negative infinity, plug a # very close. We write a + or - above/below each factor.
Example:

3. Ex 2

4. Limits Approaching Infinity (Horizontal Asymptotes)
We are also interested in examining the behavior of functions as x increases or decreases without bound ( )

5. Thm- For any rational number t > 0,
as long as there isn’t a negative in a radical
Thm- For any polynomial of degree n > 0, and
then

6. Limits to infinity with a rational function
When the limit is approaching infinity and the function is a fraction of two polynomials, we have to look at the power of the numerator and denominator (The highest exponent in each).
We divide every term by the variable with the highest power
There are 3 cases

7. Limits to infinity with a rational function pt2
Case 1
The power of the numerator is bigger
In this case, the limit = +/- infinity
Example: Evaluate 7

8. Limits to infinity with a rational function pt3
Case 2:
The power of the denominator is bigger
In this case, the limit = 0
Example: Evaluate 8

9. Limits to infinity with a rational function pt4
Case 3:
The powers are the same
In this case, we must look at the coefficients of the first terms. The limit = the fraction of coefficients
Example: Evaluate 9

10. You Try
Evaluate each limit 1) 2) 3)

11. Closure
What happens when we have a rational function and the limit approaches infinity?
Describe the 3 cases
HW 2.7 #1, 9, 13, 19, 21, 27, 37, 39