Determine the value the function approaches along the indicated paths. $($If an answer does not exist, enter DNE.$)$

lim$($x$,$ y$)(0,0)$

xy $+$ y$3$x$2+$ y$2$

$($a$)$

Evaluate the limit along the x$-$axis,

y $=0.$

$($b$)$

Evaluate the limit along the y$-$axis,

x $=0.$

$($c$)$

Evaluate the limit along the path

y $=3$x$.$

Using the results from $($a$)-($c$)$ above, evaluate the limit$.$