Answer
$\lim\limits_{x\to3^+}(\dfrac{x}{3}+\cot{\dfrac{\pi x}{2}})=1.$
Work Step by Step
$\lim\limits_{x\to3^+}(\dfrac{x}{3}+\cot{\dfrac{\pi x}{2}})\to$
$\lim\limits_{x\to3^+}\dfrac{x}{3}=\dfrac{3^+}{3}=1.$
$\lim\limits_{x\to3^+}\cot{\dfrac{\pi x}{2}}=\cot{\dfrac{3^+(\pi)}{2}}=0.$
$\lim\limits_{x\to3^+}(\dfrac{x}{3}+\cot{\dfrac{\pi x}{2}})=1+0=1.$
