Limits at Infinity for Rational Function

Limits at Infinity for Rational Function - = 2 2 4 5 3 1-=...

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Limits at Infinity For Rational Functions

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x lim x →∞   =     1 0 x lim x - → ∞   =     1 0
x x k lim lim k x x → ∞ → ∞     = ⋅         1 x k lim k x →∞   = = ⋅     1 0 = 0

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For positive integer n, n x k lim x → ∞   =     0
Use the previous limits to find the limit of a rational function as x increases without bound. To do this you must first divide every term in the numerator and the denominator by x raised to the highest power of x in the denominator and then take the limit.

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x x x x x x x x x lim lim x - →∞ →∞ +   -     =     +       2 2 2 2 2 4 5 2 3 4 5 3 x x x x lim - →∞ +    

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Unformatted text preview: = 2 2 4 5 3 1-= = = + 0 0 0 1 0 1 x x x x x x x lim lim x →∞ →∞- -- + - - + = - 2 3 3 4 1 3 3 4 3 3 4 1 2 4 2- - - -= =-3 0 0 3 2 0 2 x x x x x x x lim lim x →∞ →∞- -- + - - + = - 2 3 3 4 1 3 3 4 3 3 4 1 2 4 2- - - -= =-3 0 0 3 2 0 2 Note that as , So that x x x x x x x lim lim x--→ ∞ → ∞-- + -+ = - 2 2 4 5 3 5 3 2 3 4 3 =-∞ x →-∞ x- →-∞ 5 3 x-→-∞ 5 3 3...
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This document was uploaded on 04/03/2011.

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Limits at Infinity for Rational Function - = 2 2 4 5 3 1-=...

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