Let's say you have a function $f(x) = h(x)g(x)$. You know that $h(x) \to \infty$ as $x \to \infty$, and $g(x) \to 0$ as $x \to \infty$.
How can you go about finding the limit of $f(x)$ as $x \to \infty$
Let's say you have a function $f(x) = h(x)g(x)$. You know that $h(x) \to \infty$ as $x \to \infty$, and $g(x) \to 0$ as $x \to \infty$.
How can you go about finding the limit of $f(x)$ as $x \to \infty$
Perhaps you should consider $\lim \dfrac{g(x)}{\frac{1}{h(x)}}$, as now the numerator and denominator both go to 0. So now, you can use L'Hopital's rule if they are differentiable.
Are you familiar with l'hopital's rule? If so, do you see how to rewrite your function so that it is in a form which meets the l'hopital hypotheses?