Answer
a) $5$
b) $7$
c) Limit does not exist.
Work Step by Step
Recall that if $ f $ is a polynomial function, then we have $\lim_\limits{x\to a}f(x)=f(a)$.
In order to to find the limit, we will plug $ a $ into the function and then simplify.
a) $\lim_\limits{x\to 2^{-}} (x^2+1)=2^2+1=5$
b) $\lim_\limits{x\to 2^{+}} (3x+1)=(3)(2)+1=7$
c) From part (a) and (b) $\lim_\limits{x\to 2^{-}} \neq \lim_\limits{x\to 2^{+}} $
So, the limit does not exist.
