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Question
Evaluate the following limits:
`lim_(x -> oo) (x^4 - 5x)/(x^2 - 3x + 1)`
Solution
`lim_(x -> oo) (x^4 - 5x)/(x^2 - 3x + 1) = lim_(x -> oo) (x^4[1 - (5x)/x^4])/(x^2[1 - (3x)/x^2 +1/x^2]`
= `lim_(x -> oo) (x^2 [1 - 5/x^2])/([1 - 3/x + 1/x^2])`
= `(oo [1 - 5/oo])/([1 - 3/oo + 1/oo])`
= `(oo[1 - 0])/([1 -0 + 0])`
`lim_(x -> oo) (x^4 - 5x)/(x^2 - 3x + 1) = oo`
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