Sec 1.5 Limits at Infinity Divide numerator and denominator by the largest power of x in the denominator. See anything? f(x) has a horizontal Asymptote.

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Presentation transcript:

Sec 1.5 Limits at Infinity Divide numerator and denominator by the largest power of x in the denominator. See anything? f(x) has a horizontal Asymptote at y=1.5

If the degree of the numerator is < the degree of the denominator then the limit of the rational function is 0. If the degree of the numerator is = the degree of the denominator then the limit of the rational function is the ratio of the leading coefficients. If the degree of the numerator is > the degree of the denominator then the limit of the rational function DNE.

Guidelines for Finding Limits at +- Infinity (Horizontal Asymptote Rule from Alg2Trig!) 1.If the degree of the numerator is < the degree of the denominator then the limit of the rational function is 0. HA y=0 2.If the degree of the numerator is = the degree of the denominator then the limit of the rational function is the ratio of the leading coefficients. HA 3.If the degree of the numerator is > the degree of the denominator then the limit of the rational function DNE. No HA (if degree of numerator is 1 more than the degree of the denominator, then SA y = quotient. Use long division)

Because x is NEGATIVE!