lim sin(2+x)-sin(2-x)/x

x-0

find limit if it exist

please urgent help

Given question is,limx0sin2+x-sin2-xxAfter putting limit it is coming to be 00 form so using L'hospital rule we get, limx0sin2+x-sin2-xx=limx0ddxsin2+x-sin2-xddxx=limx0cos2+x+cos2-x1Now putting the limit we get, =cos3+cos1

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