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Question

limx0tanxsinxsin3x3sinx

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Solution

limx0tanxsinxsin3x3sinx

=limx0sinxcosxsinx3sinx4sin3x3sinx=limx0sinx(1cosx1)4sin3x=14limx01cosx1sin2x

=14limx01cosxcosx1cos2x=14limx01cosx(cosx)(1cosx)(1+cosx)

=14limx01(cosx)(1+cosx)=14×11(1+1)=14×12=18


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