Find the value of each limit$.$ For nonexistent limits$,$ give the best answer from among $,-,$ DNE, and explain your reasoning. Simplify answers.

a$)\underset{x-3}{lim}\frac{4x-x^3}{x^2+9}$

b$)\underset{x5}{lim}\frac{10-2x}{x^2-x-20}$

c$)\underset{x-4^{+}}{lim}\frac{x}{\sqrt[\phantom{2}]{16-x^2}}$

d$)\underset{x3}{lim}g(x),$ where $g(x)=\{\begin{array}{ccc}(x-4{)}^2& if& x>3\\ \frac{1}{3}x+1& if& x3\end{array}$