1. Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be given by
$f(x) = \begin{cases} \frac{\sin(8x^2)}{\log(x^2 + 1)} & x \neq 0 \\ a & x = 0 \end{cases}$
where $a \in \mathbb{R}$ is a constant.
(a) Find $\lim_{x \to 0} f(x)$.
(b) For which value(s) of a does $\lim_{x \to 0} f(x)$ exist? Explain briefly.
(c) For which value(s) of a is f continuous at $x = 0$? Explain, with reference to the
definition of continuity.
