" 53."[" LA "2(sin x-sin2x)/(x^(3))],[x rarr0" as "]

lim_(x rarr0)(2sin x-sin2x)/(x^(3))

Lt_(x rarr0)(x-sin x)/(x^(3))

lim_(x rarr0)(sin x-x)/(x^(3))

lim_(x rarr0)(x-sin x)/(x^(3)) =

lim_(x rarr0)(tan2x-sin2x)/(x^(3))

lim_(x rarr0)(sin x)/(x^(2))

3. lim_(x rarr0)(sin x sin^(-1)x)/(x^(2))

If l = underset( x rarr 0) ("Lim")( x ( 1+ a cos x ) - bsin x ) /( x^(3))= underset( x rarr 0 ) ("Lim") ( 1+a cos x ) /( x^(2))- underset( x rarr 0 ) ("lim")( b sin x )/( x^(3)) , where l in R , then

lim_(x rarr0)(2sin x^(0)-sin2x^(0))/(x^(3))

lim_(x rarr0)[sin x]