If `f(x)=lim_(t->0)tan^(-1)((e^(xt)-1)/t)`, then the value of `lim_(x->0)((f(x)-x)/x^3)` is equal to:

If f(x)=lim_(nrarroo) (cos(x)/(sqrtn))^(n) , then the value of lim_(xrarr0) (f(x)-1)/(x) is

The value of lim_(x rarr0)(sin^(-1)(2x)-tan^(-1)x)/(sin x) is equal to:

The value of lim_(x rarr0)(e-(1+x)^((1)/(x)))/(tan x) is

If f(x)=lim_(t to 0)[(2x)/(pi).tan^(-1)(x/(t^(2)))] ,then f(1) is …….

If lim_(xto0) [1+x+(f(x))/(x)]^(1//x)=e^(3) , then the value of ln(lim_(xto0) [1+(f(x))/(x)]^(1//x)) is _________.

The value of lim_(xrarr0) (log_e(1+x)-x)/(x{(1+x)^(1//x)-e}) equal to

The value of lim_(x rarr0)(int_(0)^(x) xe^(t^(2))dt)/(1+x-e^(x)) is equal to