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