Consider the following statements : S_1: lim_(x->0) [x]/x is an indeterminate form (where [:] denoet greatest integer function). S_2 : lim_(x->oo)sin(3^x)/3^x=0 and S_3 : lim_(x->oo) sqrt((x-sinx)/(x+cos^2x)) does not exist. S_4 : lim_(n->oo)((n + 2)! + (n+1)!)/(n+3)!) (n in N) =0 State, in order, whether S_1,S_2,S_3,S_4 are t(or false

lim_(n->oo)((n^2-n+1)/(n^2-n-1))^(n(n-1)) is

lim_(n->oo)((n^2-n+1)/(n^2-n-1))^(n(n-1)) is

lim_(n->oo)((n^2-n+1)/(n^2-n-1))^(n(n-1)) is

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

If the value of lim_(n to oo) n^(-n^2) ((n + 1)(n + 1/3)(n + 1/(3^2)) ….(n + 1/(3^(n-1))))^(n) is e^k then k is:

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

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