# Calc02_2 - 2.2 Limits Involving Infinity Greg Kelly Hanford...

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2.2 Limits Involving Infinity Greg Kelly, Hanford High School, Richland, Washington

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( 29 1 f x x = 1 lim 0 x x x = As the denominator gets larger, the value of the fraction gets smaller. There is a horizontal asymptote if: ( 29 lim x f x b x = or ( 29 lim x f x b g - =
2 lim 1 x x x x + Example 1: 2 lim x x x x = This number becomes insignificant as . x x ° lim x x x x = 1 = There is a horizontal asymptote at 1.

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( 29 sin x f x x = Example 2: sin lim x x x →∞ Find: When we graph this function, the limit appears to be zero. 1 sin 1 x - ≤ so for : 0 x 1 sin 1 x x x x - 1 sin 1 lim lim lim x x x x x x x - sin 0 lim 0 x x x →∞ by the sandwich theorem: sin lim 0 x x x →∞ =
Example 3: 5 sin lim x x x x →∞ + Find: 5 sin lim x x x x x →∞ + sin lim5 lim x x x x →∞ →∞ + 5 0 + 5

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Infinite Limits: ( 29 1 f x x = 0 1 lim x x + = ∞ As the denominator approaches zero, the value of the fraction gets very large.
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