Mathematics

Problem

Let

h(x)= \begin{cases} \dfrac{k}{(x-3)^2}, & x<3,\\ mx+1, & x\ge 3, \end{cases}

where

k

and

m

are real constants. Determine the values of

k

and

m

for which

\displaystyle\lim_{x\to 3} h(x)

exists and

h

is continuous at

x=3