If `L=("lim")_(xvecoo)(2x3^2x2^3x3^4 x2^(n-1)x3^n)^1/((n^(2+1))` , then the value of `L^4` is

If L=-lim_(ntooo) (2xx3^(2)xx2^(3)xx3^(4)...xx2^(n-1)xx3^(n))^((1)/((n^(2)+1))) , then the value of L^(4) is _____________.

If lim _(xto1)(x^(1)+x^(2)+x^(3)+"..."+x^(n)-n)/(x-1)=820,(nin N) then the value of n is equal to

If L=lim_(x rarr0)(e^(-((x^(2))/(2)))-cos x)/(x^(3)sin x), then the value of (1)/(3L) is

If L= lim_(xto2) (root(3)(60+x^(2))-4)/(sin(x-2)) , then the value of 1//L is________.

If L=lim_(xto0) (e^(-x^(2)//2)-cosx)/(x^(3)sinx) , then the value of 1//(3L) is ________.

If L=lim_(x rarr2)((10-x)^((1)/(3))-2)/(x-2), then the value of (1)/(4L)| is

Let L_(1)=lim_(x rarr0)((sin(2x)+cos(x)-1)/(x)) , L_(2)=lim_(x rarr oo)(sqrt(x^(2)-x)-x) , and L_(3)=lim_(x rarr4)(x^(2)-3x)/(x^(2)-x) , then the value of L_(1)L_(2)+(1)/(L_(3)) is

If f:(0,oo)rarr N and f(x)=[(x^(2)+x+1)/(x^(2)+1)]+[(4x^(2)+x+2)/(2x^(2)+1)]+[(9x^(2)+x+3)/(3x^(2)+1)]...+[(n^(2)x^(2)+x+n)/(nx^(2)+1)],n in N." Then lim_(n rarr oo)((f(x)-n)/((f(x))^(2)-(n^(3)(n+2))/(4)))=l, then the value of l^(10)-10^(l) is (where [.] denotes G.I.F and N set of natural numbers)

If I_(n)=int_(0)^(1)(1+x+x^(2)+....+x^(n-1))(1+3x+5x^(2)+....+(2n-3)x^(n-2)+(2n-1)x^(n-1))dx,n in N, then the value of sqrt(I_(9)) is