1. ## find the limit

$
\displaystyle \lim_{x\rightarrow -\infty} {e}^{4x} \sin x
$

2. Originally Posted by razemsoft21
$
\displaystyle \lim_{x\rightarrow -\infty} {e}^{4x} \sin x
$
Use the fact that $-1 \leq \sin (x) \leq 1$ and consider the behaviour of $e^{4x}$.

3. i've seen many of these problems and it seems the people who ask them never remember this useful fact:

let $a_n\to0$ as $n\to\infty,$ then if $b_n$ is bounded, we have $a_nb_n\to0$ as well.