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Question
Evaluate the following limit :
`lim_(x -> 3) [(x^2 + 2x - 15)/(x^2 - 5x + 6)]`
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Solution
`lim_(x -> 3) [(x^2 + 2x - 15)/(x^2 - 5x + 6)]`
= `lim_(x -> 3) ((x + 5)(x - 3))/((x - 2)(x - 3))`
= `lim_(x -> 3) (x + 5)/(x - 2) ...[(because x -> 3"," therefore x ≠ 3),(therefore x + 3 ≠ 0)]`
= `(lim_(x -> 3) (x + 5))/(lim_(x -> 3) (x - 2))`
= `(3 + 5)/(3 - 2)`
= 8
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