Find `underset( x rarr0 ) ( "Lim") ( tan x - sin x )/( x^(3))`

Find underset( x rarr 0 ) ( "Lim") ( e^(sin x) -sin x -1)/( x^(2))

Find underset( x rarr 0 ) ( "Lim") ( e^(sinx) -sin x -1)/( x^(2))

Evaluate underset( x rarr0 ) ( "Lim") ( 3 sin x - sin 3x)/( x- sin x )

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

Evaluate underset( x rarr0 ) ( "Lim")( e^(x) - e^(-x)-2x)/( x - sin x )

For x gt 0, underset( x rarr 0) ( "Lim") [ ( sin x)^(1//x) + ((1)/( x))^("sinx ) ] is

Evaluate : underset( x rarr0 ) ("lim") ( sqrt( ( 1+sin 3x))-1)/(ln ( 1+ tan 2x))

Evaluate underset(x rarr 0)Lt (tan x-sin x)/(x^3)

If underset(x rarr 0)lim (2a sin x - sin 2x)/(tan^(3)x) exists and is equal to 1, then the value of a is -

Evaluate underset(x rarr 0 ) ("lim") [ ( sin^(-1) x )/( x ) ] ( where [ ** ] denotes the greatest integer function ) .