Answer
From the graph we find that:
(a)
$$
\lim\limits_{x \to 2^{-}} h(x)=1
$$
(b)
$$
\lim\limits_{x \to 2^{+}} h(x)=1
$$
(c)
$$
\lim\limits_{x \to 2} h(x) =1
$$
the limit exist since,
$$
\lim\limits_{x \to 2^{-}} h(x)=\lim\limits_{x \to 2^{+}} h(x)=1
$$
(d)
From the graph we find that:
$$
h(2)
$$
does not exist since the graph has no point with an $x$-value of 2.
Notice in the figure that at a point 2 where the function is
discontinuous.
Work Step by Step
From the graph we find that:
(a)
$$
\lim\limits_{x \to 2^{-}} h(x)=1
$$
(b)
$$
\lim\limits_{x \to 2^{+}} h(x)=1
$$
(c)
$$
\lim\limits_{x \to 2} h(x) =1
$$
the limit exist since,
$$
\lim\limits_{x \to 2^{-}} h(x)=\lim\limits_{x \to 2^{+}} h(x)=1
$$
(d)
From the graph we find that:
$$
h(2)
$$
does not exist since the graph has no point with an $x$-value of 2.
Notice in the figure that at a point 2 where the function is
discontinuous.