We have to evaluate the limit of the given function:

\(\lim_{(x,y)\rightarrow(2,-1)}(xy^8-3x^2y^3)\)

Solve:

\(\lim_{(x,y)\rightarrow(2,-1)}(xy^8-3x^2y^3)\)

\(\Rightarrow(2\times(-1)^8-3(2)^2(-1)^3)\)

\(\Rightarrow(2-(-12))\)

\(\Rightarrow14\)

\(\because\lim_{(x,y)\rightarrow(2,-1)}(xy^8-3x^2y^3)=14\)

\(\lim_{(x,y)\rightarrow(2,-1)}(xy^8-3x^2y^3)\)

Solve:

\(\lim_{(x,y)\rightarrow(2,-1)}(xy^8-3x^2y^3)\)

\(\Rightarrow(2\times(-1)^8-3(2)^2(-1)^3)\)

\(\Rightarrow(2-(-12))\)

\(\Rightarrow14\)

\(\because\lim_{(x,y)\rightarrow(2,-1)}(xy^8-3x^2y^3)=14\)