Question

find the limit if this exists;
lim(x,y)-->(inf,2) (xy - 3)/(x^3 + y^3)

Answer 1

\[\lim_{(x,y) \rightarrow (\inf,2)} \frac{ (xy-3) }{ x^3+y^3 }\] divide and factorize by x
\[\lim_{(x,y) \rightarrow (\inf,2)} \frac{ x(y-3/x) }{ x^3+y^3 }\]
that is equal to
\[\lim_{(x,y) \rightarrow (\inf,2)} \frac{ (y-3/x) }{ x^2+y^3/x }\]
in the part above y tends to 2 and 3/x tends to 0
in the bottom, x^2+y^3/x tends to infinity
so a number/infinite tends to 0 and so does your limit xD (you can also do this using the definition but, i reaaaallllllyyyy don't want to do so xD)