" 3.Evaluate ":lim_(n rarr oo)(1)/(n^(2))sum_(k=0)^(n-1)[k int_(k)^(k+1)sqrt((x-k)(k+1-x))dx]

Evaluate: lim_ (n rarr oo) (1) / (n ^ (2)) sum_ (k = 0) ^ (n-1) [k int_ (k) ^ (k + 1) sqrt ((xk) (k + 1-x)) dx]

lim_(n rarr oo) 1/n^(3) sum_(k=1)^(n) k^(2)x =

Evaluate ("lim")_(n rarr oo)sum_(k=1)^nk/(n^2+k^2)

Evaluate ("lim")_(n rarr oo)sum_(k=1)^nk/(n^2+k^2)

Lt_(x to oo) (1)/(n^(3)) sum_(k=1)^(n)[k^(2)x]=

lim_ (n rarr oo) sum_ (k = 0) ^ (n) ((1) / (nC_ (k)))

Evaluate lim_(n rarr oo)sum_(k=1)^(n)quad (k)/(n^(2)+k^(2))