Consider the relationship involving g(x).
8x ≤ g(x) ≤ 4x^4 - 4x^2 + 8 for all x
Evaluate the following limit.
This is a straightforward application of the sandwich theorem.
Note that if
$\displaystyle 8x \leq g(x) \leq 4x^4 - 4x^2 + 8$ for all $\displaystyle x$, then
$\displaystyle \lim_{x \to 1}8x \leq \lim_{x \to 1}g(x) \leq \lim_{x \to 1}(4x^4 - 4x^2 + 8)$
$\displaystyle 8 \leq \lim_{x \to 1}g(x) \leq 8$.
What does this tell you about $\displaystyle \lim_{x \to 1}g(x)$?