# $\lim\limits_{x\to 0}(1+ax)^{\Large\frac{b}{x}}$=

$(a)\;e^{ab}\qquad(b)\;e^{a+b}\qquad(c)\;e^{a/b}\qquad(d)\;e$

$\lim\limits_{x\to 0}(1+ax)^{b/x}$
$\Rightarrow \big[\lim\limits_{x\to 0}(1+ax)^{\Large\frac{1}{ax}}\big]^{ab}$
$\Rightarrow e^{ab}$
Hence (a) is the correct answer.