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 $x \to \infty$
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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?
Gerry Myerson
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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.
davidlowryduda
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This won't work too well if, say, $h(x)=x$ and $g(x)=e^{-x}$, but I guess we have to let Angada work out some of the answer. – Gerry Myerson Oct 01 '11 at 01:15
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Very True. ${}{}{}$ – davidlowryduda Oct 01 '11 at 02:11