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Question

limx0tanxsinxsin3x

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Solution

Wehavelimx0tanxsinxsin3x=limx0sinxcosxsinxsin3x=limx0sinxsinx.cosxsin3x=limx0sinx(1cosx)cosx.sin3x=limx01cosxcosx.sin2x=limx01cosxcosx(1cos2x)=limx01cosxcosx(1+cosx)(1cosx)=limx01cosx(1+cosx)=1cos0(1+cos0)=11(1+1)=12

Hence, this is the answer.

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