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Q)

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

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

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