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$\lim\limits_{x \to \infty}f(x)=4$
is okay, of course. "lim" takes an argument -- otherwise it's like writing $\sqrt{}$, or $\sin{}$.
square root of what? sine of what?
\[ f(x)=\frac{(2x^2 + 1)^2}{(x - 1)^2(x^2 + x)} \]
(Did I mention that it possesses symmetry?)
(Remind me again: What's the first thing to notice?)
\[ \frac{x}{\sqrt{x^2+1}} \]
I'll have to ask questions that cover several sections at a time.
Then we began section 3.7, with a classic example: packaging. Making a box with a fixed quantity of material that holds the most it can (maximizing volume).
I'll start with any questions you might have about the material for the exam.
Then we'll continue with that very important section 3.7 -- optimization problems. The best way to explain is to do some examples, but the point is that we're going to be looking for extrema of functions. There are thus two things to do: