Let f(x)=underset(n to oo)lim[(n^(n)(x+n...

Let `f(x)=underset(n to oo)lim[(n^(n)(x+n)(x+(n)/(2))…(x+(n)/(n)))/(n!(x^(2)+n^(2))(x^(2)+(n^(2))/(4))…(x^(2)+(n^(2))/(n^(2))))]^((x)/(n))` for all `x gt 0`. Then,

A

`f((1)/(2))gef(1)`

B

`f((1)/(3))lef((2)/(3))`

C

`f'(2)le0`

D

`(f'(3))/(f(3))ge(f'(2))/(f(2))`

Verified by Experts

Similar Questions

Explore conceptually related problems

underset(n to oo)lim(((n+1)(n+2)...3n)/(n^(2n)))^((1)/(n)) is equal to

(x^(2^(n-1))+y^(2^(n-1)))(x^(2^(n-1))-y^(2^(n-1)))=

(x^(2^n)-y^(2^n))/(x^(2^(n-1))+y^(2^(n-1)))=

(d^n)/(dx^n)(logx)=? (a) ((n-1)!)/(x^n) (b) (n !)/(x^n) (c) ((n-2)!)/(x^n) (d) (-1)^(n-1)((n-1)!)/(x^n)

Show : underset(xrarr2)"lim"((1+x)^(n)-3^(n))/(x-2)=n.3^(n-1)

Prove that , (x^(n))/(n!)+(x^(n-1).a)/((n-1)!1!)+(x^(n-2).a^(2))/((n-2)!2!)+(x^(n-3).a^(3))/((n-3)!3!)+.......(a^(n))/(n!)=(x+a)^(n)/(n!)

Prove that, int_(0)^(2pi)(xsin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx=pi^(2) .

Let for all xgt0,f(x)=lim_(nto oo)n(x^((1)/(n))-1) , then

The value of lim_(xtooo) ((2^(x^(n)))e^((1)/(x))-(3^(x^(n)))e^((1)/(x)))/(x^(n)) (where n in N ) is

If phi(x)=lim_(nrarrinfty)(x^(2n)f(x)+g(x))/(1+x^(2n)) , then