The value of `lim_(xto0) (2^(3x)-3^(2x))/x` is

Answer

C

Explanation

`underset(xtooo)lim(root(3)(x^(3)+2x^(2))-sqrt(x^(2)+x))`
`=underset(xtooo)limx[(1+(2)/(x))^((1)/(3))-(1+(1)/(x))^((1)/(2))]`
`=underset(xtooo)limx[(1+(1)/(3).(2)/(x)+...)-(1+(1)/(2).(1)/(x)+...)]`
`=underset(xtooo)limx((2)/(3x)-(1)/(2x))`
`=(1)/(6)`