If `(n^(n))/(n!)=(nx)/((n-1)!), x =`

If y=((x)/(n))^(nx)(1+(log x)/(n)), then y'(n) is given by

Let f(x)=lim_(n rarr oo)[((nx+1)(nx+2)(nx+3)......(nx+n))/(n!)]^((1)/(n)) for all x>0 on the basis of above information,answre the following questions lim_(n rarr oo)x(1(x))/(f(x)) is equal to

If (f(x))^(n) =f(nx), then (f'(nx))/(f'(x)) is equal to ( where n in N)

Let C_(n)= int_(1//n+1)^(1//n)(tan^(-1)(nx))/(sin^(-1) (nx)) dx , "then " lim_(n rarr infty) n^(n). C_(n) is equal to

Let C_(n)= int_(1//n+1)^(1//n)(tan^(-1)(nx))/(sin^(-1) (nx)) dx , "then " lim_(n rarr infty) n^(n). C_(n) is equal to

If the period of ( cos ( sin(nx)))/(tan""(x//n)), n in N is 6pi then n=

If n in N, and the period of (cos nx)/(sin((x)/(n))) is 4 pi then

If f(x) =1 + nx+ (n(n-1))/(2) x^(2) + (n(n-1)(n-2))/(6) x^(3) + ...+ n^(x) , "then" f''(1) is equal to

If f(x)=1+nx+(n(n-1))/2x^(2)+(n(n-1)(n-2))/6x^(3)+………………+x^(n), then f^(")(1)=

If A=([x,x],[x,x]) then A^(n)(n in N)= 1) ([2^nx^n,2^nx^n],[2^nx^n,2^nx^n]) 2) ([2^(n-1) x^n,2^(n-1) x^n],[2^(n-1) x^n,2^(n-1) x^n]) 3) I 4) ([2^(n) x^(n-1),2^(n) x^(n-1)],[2^(n) x^(n-1),2^(n) x^(n-1)])