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Question
Evaluate the following :
`lim_(x -> ∞) [(7x^2 + 5x - 3)/(8x^2 - 2x + 7)]`
Solution
`lim_(x -> ∞) (7x^2 + 5x - 3)/(8x^2 - 2x + 7)`
= `lim_(x -> ∞) ([(7x^2 + 5x - 3)/(x^2)])/([(8x^2 - 2x + 7)/(x^2)])`
= `lim_(x -> ∞) ([7 + 5/x - 3/x^2])/([8 - 2/x + 7/x^2])`
= `(lim_(x -> ∞) 7 + lim_(x -> ∞) 5/x^2 - lim_(x -> ∞) 3/x^2)/(lim_(x -> ∞) 8 - lim_(x -> ∞) 2/x + lim_(x -> ∞) 7/x^2)`
= `(7 + 0 - 0)/(8 - 0 + 0) ...[because lim_(x -> ∞) 1/x^"k" = 0, "k" > 0]`
= `7/8`
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