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

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Answer 1 · 2015-11-04T05:31:28

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 $e^3$

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