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