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Question

limxπ2 2-1+ sin xcos2x

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Solution

limxπ2 2-1+sin xcos2 xRationalising the numerator:=limxπ2 2-1+sin x 2+1+sin xcos2 x×2+1+sin x=limxπ2 2-1+sin xcos2 x·2+1+sin x=limxπ2 1-sin x1-sin x 1+sin x 2+1+sin x=11+1 2+2=12×22=142

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