EXAMPLE $5$ Evaluate

lim$($x$,$ y$)(5,4)($x$2$y$3$ x$3$y$2+3$x $+5$y$).$

SOLUTION Since

f$($x$,$ y$)=$ x$2$y$3$ x$3$y$2+3$x $+5$y

is a polynomial, it is continuous everywhere, so we can find its limit by direct substitution:

lim$($x$,$ y$)(5,4)($x$2$y$3$ x$3$y$2+3$x $+5$y$)$

$=5235342+35+4$

$=$