Determine if the limits

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

exist by changing the problem to polar coordinates. Use the fact that

r$0+$

as

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

in your work. There are several different situations that can arise. First, if the limit blows up or depends on $$ as

r$0+$

then the limit does not exist. Second, if there is a function

g$($r$)$

such that

$|$f$($r cos$(),$ r sin$())|$ g$($r$)$

for all

$($r$,)$

and

lim$$r$0+$g$($r$)=0,$

then

lim$($x$,$ y$)(0,0)$f$($x$,$ y$)=0.$

Evaluate the limit below. $($If an answer does not exist, enter DNE.$)$

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

$(4$x$3+3$y$3)$x$2+$ y$2$

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

$(4$x$3+3$y$3)$x$2+$ y$2$

$=$