Answer
a) $\lim\limits_{x \to 1}f(x) = 2$
b) $\lim\limits_{x \to 3^-}f(x) = 1$
c) $\lim\limits_{x \to 3^+}f(x) = 4$
d) limit does not exist
e) $f(3) = 3$
Work Step by Step
a) As $x$ approaches $1$ from both sides, $f(x)$ approaches 2.
b) As $x$ approaches $3$ from the left hand side, $f(x)$ approaches $1$..
c) As $x$ approaches $3$ from the right hand side, $f(x)$ approaches $4$
d) Since the left and right hand limits (from parts b and c respectively) are not equal, the limit of $f(x)$ as $x$ approaches $3$ does not exist.
e) The value of $f(x)$ at $x = 3$ is $3$ as indicated by the solid dot on the graph.
