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Question

limxπ1cosx2sin2x

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Solution

limxπ1cosx2sin2x
=limxπ1cosx2(1cos2x)×1cosx+21cosx+2
=limxπ1cosx2(1cos2x)×1cosx+21cosx+2
=limxπ(1+cosx)(1cos2x)×1cosx+21cosx+2
=limxπ1(1cosx)(1cosx+2)
=1(1(1))(1(1)+2)
=1(1+1)(1+1+2)
=12(22)=142

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