Answer
$$\lim\limits_{v\to4^+}\frac{4-v}{|4-v|}=-1$$
Work Step by Step
$$A=\lim\limits_{v\to4^+}\frac{4-v}{|4-v|}$$
We see that $|4-v|=(4-v)$ if $(4-v)\ge0$ or $v\le4$
and $|4-v|=-(4-v)$ if $(4-v)\lt0$ or $v\gt4$
In this case, since $v\to4^+$, we only consider the values of $v\gt4$. Therefore, $|4-v|=-(4-v)$
So, $$A=\lim\limits_{v\to4^+}\frac{4-v}{-(4-v)}$$$$A=\lim\limits_{v\to4^+}\frac{1}{-1}$$$$A=\lim\limits_{v\to4^+}(-1)$$$$A=-1$$
