Given that

$\underset{x1}{lim}f(x)=9,\underset{x1}{lim}g(x)=-5,\underset{x1}{lim}h(x)=0$

find each $limit,ifit$ exists. $(Ifan$ answer does not exist, enter DNE.$)$

$(a)\underset{x1}{lim}[f(x)+4g(x)]$

$(b)\underset{x1}{lim}[g(x){]}^3$

$(c)\underset{x1}{lim}\sqrt[\phantom{2}]{f(x)}$

$(d)\underset{x1}{lim}\frac{5f(x)}{g(x)}$

$(e)\underset{x1}{lim}\frac{g(x)}{h(x)}$

$(f)\underset{x1}{lim}\frac{g(x)h(x)}{f(x)}$