Answer
(a)$-1$ (b) $-2$ (c) Does not exit. (d) $2$ (e) $0$ (f) Does not exit. (g) $1$ (h) $3$
Work Step by Step
Based on the graph of the pieces-wise functions:
(a) $\lim_{t\to 0^-}f(t)=-1$
(b) $\lim_{t\to 0^+}f(t)=-2$
(c) As $\lim_{t\to 0^-}f(t)\ne \lim_{t\to 0^+}f(t)$. the limit $\lim_{t\to 0}f(t)$ does not exit.
(d) $\lim_{t\to 2^-}f(t)=2$
(e) $\lim_{t\to 2^+}f(t)=0$
(f) As $\lim_{t\to 2^-}f(t)\ne \lim_{t\to 2^+}f(t)$, the limit $\lim_{t\to 2}f(t)$ does not exit.
(g) $f(2)=1$
(h) $\lim_{t\to 4}f(t)=f(4)=3$
