$(5$ ps$)$ Given the function $h(t)=\{\begin{array}{ccc}\frac{1}{2t+3},& if& t>0\\ 7,& if& t=0\\ \frac{2}{3}t& +\frac{1}{8},if& t<mn>0</mn>\end{array},$

determine $\underset{t0}{lim}h(t).$

If the limit is Infinity or negative infinity, say so$.$ If the limit does not exist, mathematically justify why the limit does not exist. If the tabular method is utilized in your solution, you must show a minimum of three tabular values.