The limit `lim_(x->oo) (sqrt x - 1)/(sqrt 3*x - 1)` has to be determined.
Substituting `x = oo` , gives a value of `oo` for the numerator as well as the denominator. The expression is `oo/oo` which is indeterminate. l'Hopital's rule can be used here to determine the limit. Substitute the numerator and the denominator by their derivatives.
`lim_(x->oo) ((1/2)*(1/sqrt x))/sqrt 3`
As x tends to `oo` , 1/x tends to 0.
This gives the limit `lim_(x->oo) (sqrt x - 1)/(sqrt 3*x - 1) = 0`
We have given
B) 0 is most appropriate answer.