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Let $g(x)=\lim \limits_{h \to 0} \frac{\ln (x+h)-\ln (x)}{h}$. What is $g(a)$ for any fixed constant $a \gt 0$?

A

$\cfrac{1}{x}$

B

$e^a$

C

$e^x$

D

$\cfrac{1}{a}$

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