Find `lim_(n->oo) ((n-1)(n-2)(n-3))/n^3`

lim_(n->oo)2^(n-1)sin(a/2^n)

lim_(n->oo) nsin(1/n)

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

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

f'(0) = lim_(n->oo) nf(1/n) and f(0)=0 Using this, find lim_(n->oo)((n+1)(2/pi)cos^(- 1)(1/n)-n)),|cos^(-1)1/n|

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

Evaluate the following limit: (lim)_(n->oo)(1/(n^2)+2/(n^2)+3/(n^2)++(n-1)/(n^2\ ))

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

lim_(n->oo)(n(2n+1)^2)/((n+2)(n^2+3n-1)) is equal to (a)0 (b) 2 (c) 4 (d) oo

lim_(n->oo)sin(x/2^n)/(x/2^n)