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Question
Evaluate: `lim_(x -> 1/2) (4x^2 - 1)/(2x - 1)`
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Solution
Given that `lim_(x -> 1/2) (4x^2 - 1)/(2x - 1)`
= `lim_(x -> 1/2) ((2x)^2 - (1)^2)/(2x - 1)`
= `lim_(x -> 1/2) ((2x + 1)(2x - 1))/(2x - 1)`
= `lim_(x -> 1/2) (2x + 1)`
Taking limit, we have
= `2 xx 1/2 + 1`
= 1 + 1
= 2.
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