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Question
Evaluate the following limit:
`lim_(x -> 1)[(x^3 - 1)/(x^2 + 5x - 6)]`
Solution
`lim_(x -> 1)[(x^3 - 1)/(x^2 + 5x - 6)]`
= `lim_(x -> 1) ((x - 1)(x^2 + x + 1))/((x - 1)(x + 6)`
= `lim_(x -> 1)(x^2 + x + 1)/(x + 6) ...[("As" x -> 1"," x ≠ 1),(therefore x - 1 ≠ 0)]`
= `((1)^2 + 1 + 1)/(1 + 6)`
= `3/7`
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