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_(ntooo) (2xx3^(2)xx2^(3)xx3^(4)...xx2^(n-1)xx3^(n))^((1)/((n^(2)+1))) , then the value of L^(4) is _____________. (a) -1/4 (b) 1/2 (c) 1 (d) none of the above

If f(x)=(lim)_(nvecoo)(cos(x/(sqrt(n))))^n , then the value of (lim)(xvec0)(f(x)-1)/x is 0 b. 1 c. 2 d. 3//2

If L=lim_(xto0) (e^(-x^(2)//2)-cosx)/(x^(3)sinx) , 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________.

Let lim_(n->oo)((x^2+2x+3+sinpix)^n-1)/((x^2+2x+3+sinpix)^n+1) . then

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

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

If f(x)=lim_(n->oo)[2x+4x^3+6x^5++2n x^(2n-1)] (0ltxlt1) then int f(x)dx is equal to:

lim_(x->0)((1^x+2^x+3^x+....+n^x)/n)^(1/x)

If f(x)=(lim)_(nvecoo)(3/2+[cosx](sqrt(n^2+1)-sqrt(n^2-3n+1))) where [y] denotes largest integer lt=, then identify the correct statement(s). ("lim")_(nvecoo)f(x)=0 ("lim")_(nvecpi/2)f(x)=(3pi)/4 f(x)=(3x)/2AAx in [0,pi/2] f(x)=0AAx in (pi/2,(3pi)/2)