Answer
$\dfrac{-1}{16}$
Work Step by Step
Recall that if $ f $ is a polynomial function, then we have $\lim_\limits{x\to a}f(x)=f(a)$.
In order to to find the limit, we will plug $ a $ into the function and then simplify.
$\lim_\limits{x\to 0} \dfrac{\dfrac{1}{x+4}-\dfrac{1}{4}}{x}=\lim_\limits{x\to 0} \dfrac{\dfrac{-x}{4(x+4)}}{x}$
or, $= \lim_\limits{x\to 0} \dfrac{-1}{4(x+4)}$
or, $= \dfrac{-1}{16}$
