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Question
Evaluate the following limits:
`lim_(x -> oo) 3/(x - 2) - (2x + 11)/(x^2 + x - 6)`
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Solution
`lim_(x -> oo) 3/(x - 2) - (2x + 11)/(x^2 + x - 6) = lim_(x -> oo) (3/(x - 2) - (2x + 11)/((x + 3)(x - 2)))`
= `lim_(x -> oo) (3(x + 3) - (2x + 11))/((x + 3)(x - 2))`
= `lim_(x -> oo) (3x + 9 - 2x - 11)/((x + 3)(x - 2))`
= `lim_(x -> oo) (x - 2)/((x + 3)(x - 2))`
= `lim_(x -> oo) 1/(x + 3)`
= `1/oo`
`lim_(x -> oo) 3/(x - 2) - (2x + 11)/(x^2 + x - 6)` = 0
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