Answer
(a) $\lim_{t\to4^+}(t-[t])=0$
(b) $\lim_{t\to4^-}(t-[t])=1$
Work Step by Step
The graph is shown below.
(a) $$\lim_{t\to4^+}(t-[t])$$
Looking at the graph, we see that as $t$ approaches $4$ from the right, $f(t)=t-[t]$ approaches $0$.
Therefore, $$\lim_{t\to4^+}(t-[t])=0$$
(b) $$\lim_{t\to4^-}(t-[t])$$
Looking at the graph, we see that as $t$ approaches $4$ from the left, $f(t)=t-[t]$ approaches $1$.
Therefore, $$\lim_{t\to4^-}(t-[t])=1$$
