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!
2026-03-28 14:00:30.1774706430
Finding $\lim_{t\to 0}\frac{|t-2|}{t}$ and $\lim_{t\to \infty}\frac{|t-2|}{t}$
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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
$$\lim_{t\to \infty}\frac{|t-2|}{t}=\lim_{t\to\infty}\frac{t-2}{t}.$$