Evaluate the following limit : `(lim)_(n->oo)(n/(n+y))^n`

Evaluate the following limit : (lim)_(x->oo)(logx)/(x^n),\ n >0

Evaluate the following limit: lim_(nto oo)[(n!)/(n^(n))]^(1//n)

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

Evaluate the following limit: (lim)_(n rarr oo)((n+2)!+(n+1)!)/((n+2)!-(n+1)!)

Evaluate the following limit: (lim)_(n rarr oo)(1^(3)+2^(3)+n^(3))/((n-1)^(4))

Evaluate the following limit: (lim)_(n rarr oo)2^(n-1)sin((a)/(2^(n)))

Evaluate the following limits : lim_(n to 2)(n^(3)-8)/(n^(2)-4)

Evaluate the following limit: (lim)_(n rarr oo){sqrt(x+1)-sqrt(x)}sqrt(x+2)

Evaluate the following (i) lim_(n to oo)((1)/(n^(2))+(2)/(n^(2))+(3)/(n^(2))....+(n-1)/(n^(2))) (ii) lim_(n to oo)((1)/(n+1)+(1)/(n+2)+....+(1)/(2n)) (iii) lim_(n to oo)((n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+....+(n)/(2n^(2))) (iv) lim_(n to oo)((1^(p)+2^(p)+.....+n^(p)))/(n^(p+1)),pgt0

Evaluate the following limit: quad sin((a)/(2^(n)))(lim)_(n rarr oo)(sin((a)/(2^(n))))/(sin((b)/(2^(n))))