# How do you determine the limit of (3/x^3) ((x-2)/(x-1)) as x approaches 1-?

May 19, 2018

${\lim}_{x \rightarrow {1}^{-}} \frac{3}{x} ^ 3 \cdot \left(\frac{x - 2}{x - 1}\right) = - \infty$

#### Explanation:

${\lim}_{x \rightarrow {1}^{-}} \frac{3 \left(x - 2\right)}{{x}^{3} \left(x - 1\right)} =$

${\lim}_{x \rightarrow {1}^{-}} \frac{3}{x} ^ 3 \cdot \left(\frac{x - 2}{x - 1}\right) = - \infty$

because

$x \to {1}^{-}$ $\iff$ $x - 1 < 0$ so ${\lim}_{x \rightarrow {1}^{-}} \frac{1}{x - 1} {=}^{\left(\frac{1}{0} ^ \left(-\right)\right)} = - \infty$