Consider the following limit$.$

$\underset{x-}{lim}\frac{6x}{\sqrt[\phantom{2}]{x^2+6}}$

$($a$)$ Use the definition of limits at infinity to find the value of $N$ that corresponds to $=0\mathrm{.}5.$

$N=$

$($b$)$ Use the definition of limits at infinity to find the value of $N$ that corresponds to $=0\mathrm{.}1.$

$N=$