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Question

Evaluate: limx2x2x+22

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Solution

limx2x2x+22, Rationalizing the denominator we get
limx2(x2)(x+2+2)(x+22)(x+2+2)
limx2(x2)(x+2+2)(x+2)4=limx2(x2)(x+2+2)(x2)
=2+2+2=4

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