This is the last problem on a take home quiz I was given. I keep staring at it, but I'm not really even sure how to start.

Determine all possible values of $\displaystyle a$ and $\displaystyle b$ if

$\displaystyle \lim_{x\to\0} \frac{a+cos(bx)}{2x^2} = -9$

I've done some searching, and found 2 instances of a similar problem:

Yahoo! Canada Answers - Find Numbers a and b for a limit?

Find numbers a and b? - Yahoo! Answers

In both of those problems, the denominator in the limit is only X, so they state that as x->0, the numberator must be equal to zero as well.

Ok, so

$\displaystyle a+cos(by)=0$

in both the examples that I have found, the person working it out would put in a 0 for a at this point. Ok, but If I do that,

$\displaystyle cos(by)=0$ or $\displaystyle cos(by)=-a$

That cannot be broken up anymore. In the examples, after finding b using this method, they use it to find other values. But without a way to isolate b I'm stuck.

Thanks in advance for any help.