Evaluate: `underset(x rarr 0)("lim") ((729)^x-(243)^x-(81)^x+9^x+3^x-1)/(x^3)`

Evaluate: lim_underset(x rarr 0) (sqrt(1+x+x^(2)+x^(3))-1)/(x) .

underset( x rarr 0 ) ("Lim") [ ((1+x)^(1//x))/( e ) ]^(1//x)

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

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") ( sqrt( ( 1+sin 3x))-1)/(ln ( 1+ tan 2x))

underset( x rarr 0 ) ( "Lim") ((x- 1+ cos x )/( x))^((1)/( x))

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

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

The value of underset( x rarr 0^(+))( lim) (cos^(-1) ( x- [x]^(2) ). sin^(-1) (x- [ x] ^(2)))/(x- x^(3)) , where [x] denotes the greatest integer le x is :