I am new at here and am having a problem in using piecewise function to evaluate the absolute value in following limits calculation.
$\displaystyle \lim_{x→a^-} \frac{a}{|a-x|}$ (where $a \leq 0$)
For denominator $|y-x|$, I tried the piecewise function as below:
1) $-(a-x), x \geq 0$ (e.g. $-(-2-(-1))$)
2) $(a-x), x \leq 0$ (e.g. $(-2-(-1))$)
But I feel that the piecewise results are wrong as $x$ can never be positive because of the condition that $(a \leq 0)$ and $(x \leq a)$. Do I wrongly use the piecewise function to resolve the formula?