[" Let "A_(n)=int_((1)/(n+1))^((1)/(n))(tan^(-1)nx)/(sin^(-1)nx)dx" and "],[lim_(n rarr oo)n^(2)A_(n)=L" then "(L/2)=]

Let C_ (n) = int _ ((1) / (n) +1) ^ ((1) / (n)) (tan ^ (- 1) (nx)) / (sin ^ (- 1) (nx) ) dx then lim_ (n rarr oo) n ^ (2) C_ (n) =

Let C_(n)= int_(1//n+1)^(1//n)(tan^(-1)(nx))/(sin^(-1) (nx)) dx , "then " lim_(n rarr infty) n^(n). C_(n) is equal to

Let C_(n)= int_(1//n+1)^(1//n)(tan^(-1)(nx))/(sin^(-1) (nx)) dx , "then " lim_(n rarr infty) n^(n). C_(n) is equal to

int_(0)^((pi)/(2n))(dx)/(1+Cot^(n)nx)=

Let a_(n)=sum_(k=1)^(n)tan^(-1)((1)/(k^(2)+k+1));n>=1 ,then lim_(n rarr oo)n^(2)(e^(a_(n)+1)-e^(a_(n)))=

Let: a_(n)=int_(0)^((pi)/(2))(1-sin t)^(n)sin2tdt Then find the value of lim_(n rarr oo)na_(n)

lim_(n to oo)(int_(1//(n+1))^(1//n)tan^(-1)(nx)dt)/(int_(1//(n+1))^(1//n)sin^(-1)(nx)dx) is equal to

Let a_(n)=int_(0)^((pi)/(2))(1-cos2nx)/(1-cos2x)dx , then a_(1),a_(2),a_(2),"………." are in

a_ (n) = int_ (0) ^ ((pi) / (2)) (1-sin t) ^ (n) sin2tdt ten lim_ (n rarr oo) sum_ (n = 1) ^ (n) (a_ ( n)) / (n) is equal to