`Lim _(n rarr infty) sin n`

If [[cos theta,sin theta],[-sin theta,cos theta]], then lim _(n rarr infty )A^(n)/n is (where theta in R )

The value of lim_(n rarr infty) (1)/(n) {(n+)(n+2)(n+3)…(n+n)}^(1//n) is equal to

Let L= lim_(nrarr infty) int_(a)^(infty)(n dx)/(1+n^(2)x^(2)) , where a in R, then L can be

Define a sequence {S_(n)} of real numbers by S_(n) = sum_(k=0)^(n) (1)/(sqrt(n^(2)+k)) , for n ge 1 . Then lim_(n rarr infty) S_(n)

Let f(x) = {{:((x)/(sin x) ",",x in "(0,1)"),(1",",x=0):} Consider the integral I_(n) = sqrt(n)int_(0)^(1//n) f(x)e^(-n x)dx . Then lim_(n rarr infty) I_(n)

lim_(n rarr infty ) [((n+1)(n+2)...3n)/(n^(2n))]^(1//n) is equal to