# Determine the limit of each function analytically. Show neat and complete soluti

Joni Kenny 2021-10-12 Answered
Determine the limit of each function analytically. Show neat and complete solution. (hint: some of the items need to be factored or rationalized for the limits to exist)
$\underset{x\to 2}{lim}\frac{{\left(3x-2\right)}^{2}-{\left(x+2\right)}^{2}}{\left(x-2\right)}$
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## Expert Answer

Latisha Oneil
Answered 2021-10-13 Author has 100 answers
$\underset{x\to 2}{lim}\frac{{\left(3x-2\right)}^{2}-{\left(x+2\right)}^{2}}{\left(x-2\right)}$
$=\underset{x\to 2}{lim}\frac{\left(3x-2+x+2\right)\left(3x-2-x-2\right)}{\left(x-2\right)}$
$=\underset{x\to 2}{lim}\frac{4x\left(2x-4\right)}{x-2}=\underset{x\to 2}{lim}\frac{4x\cdot 2\left(x-2\right)}{\left(x-2\right)}$
$=8\underset{x\to 2}{lim}\left(x\right)$
$=8×2=16$
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