Section 12.4.

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Presentation transcript:

Section 12.4

Limits at Infinity and Limits of a Sequence If the graph has a horizontal asymptote, then the limit as x approaches infinity or negative infinity is the horizontal asymptote. If the largest exponent is in the denominator, then the horizontal asymptote is y = 0. This means the limit as x approaches infinity or negative infinity is 0.

Limits at Infinity and Limits of a Sequence If the largest exponent in the numerator and denominator are the same, then the horizontal asymptote is y = (leading coefficient)/(leading coefficient) This is also the limit as x approaches infinity or negative infinity.

Limits at Infinity and Limits of a Sequence If the largest exponent is in the numerator, then there is not a horizontal asymptote. This means that the limit as x approaches infinity or negative infinity is either infinity or negative infinity depending on the leading coefficient.

Limits at Infinity and Limits of a Sequence Since a sequence goes on for infinity, the limit of a sequence is the same as the limit as x approaches infinity.