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Question
Evaluate the following limit.
`lim_(x -> 3) (x^4 - 81)/(2x^2-5x - 3)`
Solution
`lim_(x → 3) (x^4 - 81)/(2x^2 - 5x - 3)`
= `lim_(x → 3) ((x - 3) (x + 3) (x^2 + 9))/((x - 3) (2x + 1))`
= `lim_(x → 3) ((x + 3) (x^2 + 9))/(2x + 1)`
= `((3 + 3) (9 + 9))/(6 + 1)`
= `(6 xx 18)/7`
= `108/7`
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