If `lim(n->oo)(n*3^n)/(n(x-2)^n +n*3^(n+1)-3^n) = 1/3` then the range of x is (where `n epsilon N`)

If lim_(xto oo)(n.3^(n))/(n.(x-1)^(n)+n.3^(n+1)-3^(n))=1/3 , the number of the integral values of x is ………..

If lim_(nrarroo) (n*2^(n))/(n(3x-4)^(n)+n*2^(n+1)+2^(n))=1/2 where n in NN then the number of integers in the range of x is

If lim_(nrarroo) (n.2^(n))/(n(3x-4)^(n)+n.2^(n+1)+2^(n))=1/2 where "n" epsilonN then the number of integers in the range of x is

lim_(n rarr oo)(3^(n+1)+2^(n+2))/(3^(n-1)+2^(n-2)) =

lim_(x rarr2)((1+x)^(n)-3^(n))/(x-2)=n*3^(n-1)

lim_(n rarr oo)(2^(3n))/(3^(2n))=

lim_(n rarr oo)(2^(n)+3^(n))^(1/n)

lim_(n -> oo) (((n+1)(n+2)(n+3).......3n) / n^(2n))^(1/n)is equal to

lim_(n to oo) (3^(n)+4^(n))^(1//n) is equal to

lim_ (n rarr oo) ((n-1) (n-2) (n-3)) / (n ^ (3))