Answer
$\dfrac{-1}{4}$
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.
$\lim_\limits{x\to 2} \dfrac{\dfrac{1}{x}-\dfrac{1}{2}}{x-2}=\lim_\limits{x\to 2} \dfrac{\dfrac{2-x}{2x}}{x-2}$
or, $= \lim_\limits{x\to 2} \dfrac{-1}{2x}$
or, $= \dfrac{-1}{4}$
