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Question
Evaluate the following limits: `lim_(x -> -2)[(-2x - 4)/(x^3 + 2x^2)]`
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Solution
`lim_(x -> -2)[(-2x - 4)/(x^3 + 2x^2)]`
= `lim_(x -> - 2) (-2(x + 2))/(x^2 (x + 2)`
= `lim_(x -> -2) (-2)/(x^2) ...[("As" x -> - 2"," x ≠ - 2),(therefore x + 2 ≠ 0)]`
= `((-2))/(-2)^2`
= `(-2)/4`
= `(-1)/2`
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