Answer
a) $6$ b) $8$ 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) Since, $ \lim_\limits{x\to 1^{-}} x=1$ when $ x \lt 1$
$\lim_\limits{x\to 1^{-}} x+5=1+5=6$
b) Since, $ \lim_\limits{x\to 1^{+}} x=1$ when $ x \gt 1$
$\lim_\limits{x\to 1^{-}} x+7=1+7=8$
c) From part (a) and (b) $\lim_\limits{x\to 1^{-}} x+5 \neq \lim_\limits{x\to 1^{+}} x+7$
So, limit does not exist.
