if `phi(x)=lim_(x->oo) (x^n-x^-n)/(x^n+x^-n)` then `intsin^-1xphi(x)dx`

lim_(n->oo)sin(x/2^n)/(x/2^n)

lim_(x->oo)(1-x+x.e^(1/n))^n

If f(x)=lim_(n rarr oo)(x^(n)-x^(-n))/(x^(n)+x^(-n)),x>1 then int(xf(x)log(x+sqrt(1+x^(2))))/(sqrt(1+x^(2)))dx is

Let f be a positive differentiable function defined on (0,oo) and phi(x)=lim_(nrarroo) (f(x+(1)/(n))/f(x))^(n) . Then intlog_(e)(phi(x))dx=

The equivalent definition of the function f(x)=lim_(n to oo)(x^(n)-x^(-n))/(x^(n)+x^(-n)), x gt 0 , is

The equivalent definition of the function f(x)=lim_(n to oo)(x^(n)-x^(-n))/(x^(n)+x^(-n)), x gt 0 , is

If phi(x)=lim_(n->oo)(x^(2n)(f(x)+g(x)))/(1+x^(2n)) then which of the following is correct

let f(x)=lim_(n rarr oo)(x^(2n)-1)/(x^(2n)+1)

Let f(x)=lim_(n->oo)(log(2+x)-x^(2n)sinx)/(1+x^(2n)) . then

lim_ (n rarr oo) (x ^ (n)) / (n!)