Evaluate: `("lim")_(xvecoo)sin^n((2pin)/(3n+1)),n in Ndot`

Evaluate lim_(ntooo)(pin)^(2//n)

Evaluate: lim_(n rarr oo)(n^(p)sin^(2)(n!))/(n+1)

Evaluate: (lim)_(n rarr oo)[(n!)/(n^(n))]^(1/n)

Evaluate lim_(ntooo) (n^(p)sin^(2)(n!))/(n+1),"wher "0ltplt1.

Evaluate (lim)_(n->oo)n^2int_(-1//n)^(1//n)(2010 sin x+2012cosx)|x|dxdot

lim_(n rarr oo)2^(n)sin(a)/(2^(n))

If I_n=int_0^(sqrt(3))(dx)/(1+x^n),(n=1,2,3. .), then find the value of ("lim")_(nvecoo)I_ndot (a)0 (b) 1 (c) 2 (d) 1/2

Evaluate lim_(nto oo)((n+2)!+(n+1)!)/((n+2)!-(n+1)!)

Let f be differentiable at x=a\ a n d\ l e t\ f(a)!=0. Evaluate (lim)_(n->oo){(f(a+1/n))/(f(a))}^ndot