Answer
$\lim\limits_{x\to0.5^-}\frac{2x-1}{|2x^3-x^2|}=-4$
Work Step by Step
$A=\lim\limits_{x\to0.5^-}\frac{2x-1}{|2x^3-x^2|}$
$A=\lim\limits_{x\to0.5^-}\frac{2x-1}{|x^2(2x-1)|}$
$A=\lim\limits_{x\to0.5^-}\frac{2x-1}{x^2|2x-1|}$ (for $x^2\geq0\hspace{0.5cm}\forall x\in R)$
Therefore,
$A=\lim\limits_{x\to0.5^-}\frac{2x-1}{-x^2(2x-1)}$
$A=\lim\limits_{x\to0.5^-}\frac{1}{-x^2}$
$A=\frac{1}{-0.5^2}$
$A=-4$
