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lim 2sinx - sin2x
_____________________
x^3
x--> 0
_____________________ = 1
x->0 -------------------- since sin 2x=2 sinx cosx
lim 2sinx lim (1- cosx) lim sinx /x =1
x->0 ------- x->0 --------- x->0
x x^2
2 lim ( 2sin^2(x/2))/ x^2 using identity 1-cos2x = 2sin^2(x)
x->0
now ( 2sin^2(x/2))/ x^2 may be written as 2sin^2(x/2)/4 (x^2/4)
lim ( sin^2(x/2))/ (x/2)^2 = 1
thus we have 2*(2/4)=1
if u r satisfied wid the answer click on 'yes' :)
2sinx-2sinxcosx
2sinx(sinx^2{x\2}
4x^3
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