Question

What is `lim_(xrarr0) ( 1 + 3x )^(1/x)`?

Answer 1

It is

`lim_(x->0) e^(ln(1+3x)/x)`

Hence we have to calculate the limit by applying D'Hospital Law

#lim_(x->0)ln(1+3x)/x=lim_(x->0) ((d/dxln(1+3x))/(dx/dx))= lim_(x->0) 3/(1+3x)=3#

Hence the limit is `e^3`