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Question

limx0(1cos2x)sin5xx2sin3x

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Solution

limx0(1cos2x)sin5xx2sin3x
we know that
cos2x=12sin2x 2sin2x=1cosx
limx02sin2xsin5xx2sin3x
we know that sinxx=1 at x0
limx02(sinxx)2×(sin5x5x)×(3xsin3x)×5x3x
limx02×53=103

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