Find the limit of a function as $ x$ approaches $0$ How can I find the limit of $\dfrac{\cos(3x) - 1 }{x^2}$ as $x\to 0$?
If someone could please break down the steps, for clear understanding. I'm studying for the GRE. Thanks in advance !!

Since you are studying for the GRE, which if I recall correctly is a multiple choice exam, knowing L'Hospital's rule is a good thing. Here's the simple version:
When you plug in your value that $x$ is approaching, if you end up with $0/0$ or $\infty/\infty$, then you can take the derivatives of the top and bottom, and then take the limit again. Using this rule (which we have to apply twice here), 
$$\lim\limits_{x\to 0}\dfrac{\cos(3x)-1}{x^2}=\lim\limits_{x\to0}\dfrac{-3\sin(3x)}{2x}=\lim\limits_{x\to0}\dfrac{-9\cos(3x)}{2},$$
and then plugging in $0$ gives our answer, which is $-9/2$. Does this all make decent sense?
