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

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

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

Evaluate: ("lim")_(xvecoo)(sqrt(3x^2-1)-sqrt(2x^2-1))/(4x+3)

If f(x)=lim_(n->oo)((x^2+a x+1)+x^(2n)(2x^2+x+b))/(1+x^(2n))and lim_(x->+-1)f(x) exist, then The value of b is (a) -1 (b). 1 ( c.) 0 (d). 2

If L=lim_(x->0)(e^(-(x^2/2))-cosx)/(x^3 sinx), then the value of 1/(3L) is

Evaluate: ("lim")_(nvecoo)((a1 1/x+a2 1/x++a n1/x)/n)^(n x)

Let k(x)=int((x^2+1)dx)/((x^3+3x+6)^(1/3))a n dk(-1)=1/(2^(1/3)) . Then the value of k(-2) is____

If (4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r) , then the value of

If (1 - x)^(n) = C_(0) + C_(1)x + C_(2)x^(2) + ......... + C_(n)x^(n) , then the value of 1.C_(1) + 2.C_(3) + 3.C_(3) + ......... + n.C_(n) =

Evaluate ("lim")_(nvecoo){cos(x/2)cos(x/4)cos(x/8) cos(x/(2^n))}