Answer
a) $2$
b) $4$
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) $\lim_\limits{x\to 1^{-}} \sqrt[3] {x^2+7}=\sqrt[3] {1^2+7}=2$
b) $\lim_\limits{x\to 1^{+}} (4x)=4$
c) From part (a) and (b) $\lim_\limits{x\to 1^{-}} \neq \lim_\limits{x\to 1^{+}} $
So, the limit does not exist.
