$(6$ pts$)$ Given that $\underset{x4}{lim}f(x)=-1,\underset{x4}{lim}g(x)=9,$ find the following limits$.$

$($a$)\underset{x4}{lim}[x^{2}f(x)+5\sqrt[\phantom{2}]{g(x)}]$

$($b$)\underset{x4}{lim}\frac{5x(f(x){)}^2}{4f(x)+3g(x)}$