Let $h(x)=\begin{cases}kx+1, & x<3,\\[4pt]c, & x=3,\\[4pt]\dfrac{x^{2}-9}{x-3}, & x>3.\end{cases}$ …

Mathematics

Problem

Let

h(x)=\begin{cases}kx+1, & x<3,\\[4pt]c, & x=3,\\[4pt]\dfrac{x^{2}-9}{x-3}, & x>3.\end{cases}

Find the values of

k

and

c

that make

h

continuous at

x=3