Let: `a_n=int_0^(pi/2)(1-sint)^nsin2tdt` Then find the value of `lim_(n->oo)na_n`

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

Let I_(n)=int_(0)^(pi//2)(sinx+cosx)^(n)dx(nge2) . Then the value of n. I_(n)-2(n-1)I_(n-1) is

If lim_(n->oo)1/((sin^(-1)x)^("n")+1)=1 ,t h e n find the value of x.

Iff(x)=e^(g(x))a n dg(x)=int_2^x(tdt)/(1+t^4), then find the value of f^(prime)(2)

The value of lim_(ntooo) [(1+2+3+...+n)/n^2] is

The value of lim_(nto0) [(1+2+3+...+n)/n^2] is

Let f(x)=lim_( n to oo)(cosx)/(1+(tan^(-1)x)^(n)) . Then the value of int_(o)^(oo)f(x)dx is equal to

IfA_n=int_0^(pi/2)(sin(2n-1)x)/(sinx)dx ,b_n=int_0^(pi/2)((sinn x)/(sinx))^2dxforn in N , Then A_(n+1)=A_n (b) B_(n+1)=B_n A_(n+1)-A_n=B_(n+1) (d) B_(n+1)-B_n=A_(n+1)

Let the sequence {b_n} real numbers satisfies the recurrence relation b_(n+1)=1/3(2b_n+(125)/(b_n)^2),b_n!=0. Then find the (lim)_(n to oo)b_ndot

If a_1=1a n da_(n+1)=(4+3a_n)/(3+2a_n),ngeq1,a n dif("lim")_(nvecoo)a_n=a , then find the value of adot