Mathematics

Problem

Let

g

be the function defined by

g(x)= \begin{cases} \dfrac{e^{x}-1}{x}, & x<0,\\ \dfrac{\ln(1+ax)}{x}, & x>0. \end{cases}

For which value of the constant

a

does

\displaystyle\lim_{x\to 0} g(x)

exist? a)

a=e

a=0

a=1

a=\dfrac{1}{e}