`lim_(x -> oo) x^n / e^x = 0`, (n is an integer) for

lim_(x rarr oo) x^(n)/e^(x) = 0 (n is an integer) for

lim_ (x rarr oo) (x ^ (n)) / (e ^ (x)) = 0, (n is an integer) for

lim_ (n rarr oo) (x ^ (n)) / (n!)

lim_ (x rarr oo) (log x) / (x ^ (n)) =

int_(0)^(oo)x^(n)e^(-x)dx(n is a +ve integer) is equal to

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_(x->oo)(1-x+x.e^(1/n))^n

lim_ (x rarr oo) (log x ^ (n) - [x]) / (x), n in N

lim_(x rarr oo)((log x)/(x^(n)))

The least integer n for which lim_(x to 0) ((cos x - 1) (cos x - e^(x)))/(x^(n)) is a finite non-zero number is