calculus - Finding $lim_{tto 0}frac{|t-2|}{t}$ and $lim_{tto infty}frac{|t-2|}{t}$

Find

$$\lim_{t\to 0}\frac{|t-2|}{t}$$ and $$\lim_{t\to\infty}\frac{|t-2|}{t}$$

Usually I would simply the top and bottom but I'm not sure what to do for absolute values.

Any help would be appreciated. Thanks!

Answer

HINT : Note that

$$|t-2|=\begin{cases}t-2&\text{if $t-2\ge 0$}\\-(t-2)&\text{if $t-2\lt 0$}\end{cases}$$ Hence, we have $$\lim_{t\to 0}\frac{|t-2|}{t}=\lim_{t\to 0}\frac{-(t-2)}{t}$$ and

$$\lim_{t\to \infty}\frac{|t-2|}{t}=\lim_{t\to\infty}\frac{t-2}{t}.$$