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

If f(n)=int_(0)^(2015)(e^(x))/(1+x^(n))dx , then find the value of lim_(nto oo)f(n)

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

The value of lim_(n rarr oo)((1)/(2^(n))) is

l_(n)=int_(0)^(pi//4)tan^(n)xdx , then lim_(nto oo)n[l_(n)+l_(n-2)] equals

Find the value of lim_(n rarr oo)sum_(k=1)^(n)((k)/(n^(2)+k))

If lim_(n rarr oo)(prod_(r=1)^(n)sin((r pi)/(4n))cos((r pi)/(4n)))^((1)/(n))=(a)/(b) a,b in N then find the least value of (a+b)

Let P_(n)=root(n)(((3n!)/(2n!)))(n=1,2,3dots) then find lim_(n rarr oo)(P_(n))/(n)

Let f(x)=lim_(n rarr oo)(x^(2n-1)+ax^(2)+bx)/(x^(2n)+1). If f(x) is continuous for all x in R then find the values of a and b.