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Question
Evaluate the following limit :
`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^3 - 4x^2 + 4x))/(lim_(x -> 2)(x^2 - 1))`
= `(2^3 - 4(2)^2 + 4(2))/(2^2 - 1)`
= `0/3`
= 0
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