# Use limit theorems as neede to evaluate each of the following limits b) \

Use limit theorems as neede to evaluate each of the following limits
b) $\underset{x\to {2}^{-}}{lim}\frac{3{x}^{2}-5x-2}{|{x}^{3}-8|}$
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Leonard Stokes
Given,
$\underset{x\to {2}^{-}}{lim}\frac{3{x}^{2}-5x-2}{|{x}^{3}-8|}$
$\underset{x\to {2}^{-}}{lim}\frac{3{x}^{2}-5x-2}{-\left({x}^{3}-8\right)}$
$\underset{x\to {2}^{-}}{lim}\frac{3{x}^{2}+x-6x-2}{\left(-x-2\right)\left({x}^{2}+2x+4\right)}$
$\underset{x\to {2}^{-}}{lim}\frac{x\left(3x+1\right)-2\left(3x+1\right\}\left\{-\left(x-2\right)\left({x}^{2}+2x+4\right)\right\}}{}$
$\underset{x\to {2}^{-}}{lim}\frac{\left(x-2\right)\left(3x+1\right)}{-\left(x-2\right)\left({x}^{2}+2x+4\right)}$
$\underset{x\to {2}^{-}}{lim}\frac{3x+1}{-\left({x}^{2}+2x+4\right)}=\frac{7}{-12}$
Answer: $-\frac{7}{12}$
Jeffrey Jordon