Construct a table and find the indicated limit$.$

If $h(x)=\frac{\sqrt[\phantom{2}]{x}+2}{x-3},$ then find $\underset{x3}{lim}h(x).$

Complete the table below.

$($Type integers or decimals rounded to four decimal places as needed.$)$

What is the limit$?$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.\underset{x3}{lim}\frac{\sqrt[\phantom{2}]{x}+2}{x-3}=$

B$.$ The limit does not exist and is neither $$ nor $-.$