Answer
(a) -1
(b) -2
(c) $\lim\limits_{x \to 0}$g(t) does not exist because $\lim\limits_{x \to0^-}$g(t)$\ne$$\lim\limits_{x \to 0^+}$g(t)
(d) 2
(e) 0
(f) $\lim\limits_{x \to 2}$g(t) does not exist because $\lim\limits_{x \to2^-}$g(t)$\ne$$\lim\limits_{x \to 2^+}$g(t)
(g) 1
(h) 3
Work Step by Step
To approach this problem, you simply look at the graph. When the question gives you a limit, it is asking you to look and see what happens to y as x goes to the number given. If the number has a negative sign on its right, then you look from the left hand side. If it has a positive sign on its right, then you look from the right hand side. If it has no sign, then you look at it from the left and right hand side. As for the questions that ask for g(t). That means x=t and you simply have to see where y is at that x-value. If there is a hole, then that value does not exist.
