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Question
Evaluate the following limits: `lim_(x -> 2)[(x^3 - 4x^2 + 4x)/(x^2 - 1)]`
Solution
`lim_(x -> 2)[(x^3 - 4x^2 + 4x)/(x^2 - 1)]`
= `lim_(x -> 2) (x(x^2 - 4x + 4))/((x^2 - 1)`
= `lim_(x -> 2) (x(x - 2)^2)/(x^2 - 1)`
= `(2(0))/((2)^2 - 1`
= `(2 xx 0)/3`
= 0
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