# Evaluate the following limits. lim_{(x,y)rightarrow(-3,3)}(4x^2-y^2)

Evaluate the following limits.
$$\lim_{(x,y)\rightarrow(-3,3)}(4x^2-y^2)$$

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Nichole Watt
Given:
$$\lim_{(x,y)\rightarrow(-3,3)}(4x^2-y^2)$$
Solve:
$$\lim_{(x,y)\rightarrow(-3,3)}(4x^2-y^2)$$
$$=\lim_{(x,y)\rightarrow(-3,3)}(2^2x^2-y^2)$$
Apply exponent rule: $$a^nb^n=(ab)^n$$
$$\lim_{(x,y)\rightarrow(-3,3)}((2x)^2-y^2)$$
Apply $$(x^2-y^2)=(x+y)(x-y)$$
$$=\lim_{(x,y)\rightarrow(-3,3)}(2x+y)(2x-y)$$
Plug the values
$$=(2(-3)+3)(2(-3)-3)$$
$$=(-6+3)(-6-3)$$
$$(-3)(-9)$$
$$=27$$
$$=\lim_{(x,y)\rightarrow(-3,3)}(4x^2-y^2)=27$$