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Question

The value of the limit limx02 sin x sin 2xx3 is

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Solution

limx02 sin x sin 2xx3=limx02 sin x 2 sin x cos xx3=limx02 sin x (1cos x)x3=2limx0 sin xx×(1cos x)x2=2 × 1 ×limx02 sin2 (x/2)x2=limx0 sin2 (x/2)x2/4=(limx20 sin x/2x/2)2=1

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