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Evaluate : limx0 (2+x)sin(2+x)2sin2x

Solution :

limx0 2(sin(2+x)sin2)+xsin(2+x)x

= limx0(2.2.cos(2+x2)sinx2x + sin(2+x))

= limx02cos(2+x2)sinx2x2 + limx0sin(2+x)

= 2cos2 + sin2


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