Answer
$\lim\limits_{x\to0^-}\dfrac{x+2}{\cot{x}}=0.$
Work Step by Step
$\lim\limits_{x\to0^-}\dfrac{x+2}{\cot {x}}\to$
$\lim\limits_{x\to0^-}(x+2)=0^-+2=2.$
$\lim\limits_{x\to0^-}\cot{x}=\cot{0^-}=-\infty.$
$\lim\limits_{x\to0^-}\dfrac{x+2}{\cot{x}}=\dfrac{2}{-\infty}=0.$
