2.7 Limits involving infinity Wed Sept 16 Do Now Find

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:

Ex 2

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

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

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

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

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

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

You Try Evaluate each limit 1) 2) 3)

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