Question

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

Limits and continuity
ANSWERED
asked 2020-11-01
Evaluate the following limits.
\(\lim_{(x,y)\rightarrow(-3,3)}(4x^2-y^2)\)

Answers (1)

2020-11-02
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
\(=(2(-3)+3)(2(-3)-3)\)
\(=(-6+3)(-6-3)\)
\((-3)(-9)\)
\(=27\)
Answer:
\(=\lim_{(x,y)\rightarrow(-3,3)}(4x^2-y^2)=27\)
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