Discuss `underset(xrarrinfty)Lim(e^(1/x))`

Let f: R rarr R be a positive increasing function with underset(xrarrinfty)lim(f(3x))/(f(x))=1, then underset(xrarrinfty)lim(f(2x))/(f(x)) =

Evaluate: underset(xrarr0)lim (e^(log(1+2x)))/x

Evaluate underset(xrarr0)lim (e^(ax)-1)/(e^(bx)-1) .

underset(x to0)(lim)(e^(x)-1)/(x) is :

Evaluate underset(xrarr0)lim (e^(2x)-1)/(sinx) .