Evaluate the given limit: limits{x \to 2}{1}{x}+{1}{2}}{x+2}

\( \lim\limits_{x \to 2} \dfrac{\dfrac{1}{x}+\dfrac{1}{2}}{x+2}\)

At x = -2, the value of the given function takes the form \( \dfrac{0}{0}\)

Now,

= \( \lim\limits_{x \to 2} \dfrac{\dfrac{2+x}{2x}}{x+2}\)

= \( \lim\limits_{x \to 2} \dfrac{1}{2x}\)

= \(\dfrac{1}{2(-2)}=\dfrac{1}{4}\)