Mathematics

Problem

Let

p

be a function with the following properties. • For

x<2

p(x)=\sqrt{4-x}

. • For

x=2

p(2)=3

. • For

x>2

p(x)=\dfrac{1}{x-2}+1

. Determine whether

\displaystyle \lim_{x\to2} p(x)

exists. If it exists, state its value; if it does not, state “does not exist.”