Answer
$$27$$
Work Step by Step
$$\eqalign{
& \mathop {\lim }\limits_{\left( {x,y} \right) \to \left( { - 3,3} \right)} \left( {4{x^2} - {y^2}} \right) \cr
& {\text{use the law 1 }}\mathop {\lim }\limits_{\left( {x,y} \right) \to \left( {a,b} \right)} \left( {f\left( {x,y} \right) + g\left( {x,y} \right)} \right).\,\,\,\left( {{\text{see page 887}}} \right){\text{then}} \cr
& = \mathop {\lim }\limits_{\left( {x,y} \right) \to \left( { - 3,3} \right)} \left( {4{x^2}} \right) - \mathop {\lim }\limits_{\left( {x,y} \right) \to \left( { - 3,3} \right)} \left( {{y^2}} \right) \cr
& {\text{law constant multiply}} \cr
& = 4\mathop {\lim }\limits_{\left( {x,y} \right) \to \left( { - 3,3} \right)} \left( {{x^2}} \right) - \mathop {\lim }\limits_{\left( {x,y} \right) \to \left( { - 3,3} \right)} \left( {{y^2}} \right) \cr
& {\text{evaluate using the theorem 12}}{\text{.1}} \cr
& = 4{\left( { - 3} \right)^2} - {\left( 3 \right)^2} \cr
& {\text{simplifying}} \cr
& = 36 - 9 \cr
& = 27 \cr} $$
