Okay, I've checked about ten different sites for an answer to this, and about half said one thing, while the other half disagreed, so I want a definitive answer:
I know that 0/0 is undefined, but what I have are two equations:
f(x)=0
And:
g(x)=0
Where both zeros are of the same density.
Now correct me if I'm wrong, but isn't this a point where I can say:
lim(n approaches x) [(g(n))/(f(n))]=1
TPH is right, the answer is no. the closest thing to what you may want is a limit existing if both the numerator and denominator go to zero, for example . but of course, this is not always true, . so limits might exists, but will not always be 1, they can be anything, however 0/0 is always undefined
rman144, maybe you are confused about the concept of limit of the quotient of 2 functions that tends to 0 in a point and the number 0 divided by 0. What you call "same density" would be that the 2 functions tends to 0 at almost the same "speed".
For example, if and . The limit of the quotient of both function will give when tends to . But it doesn't mean that because and the limit of the quotient is equal to over . If you understand the concept of limit, you know it's not true so you cannot get confused on this.
EDIT:Jhevon, you are fast! I didn't know someone would answer that fast, sorry for my post.
Back to the concept of limit : rman144. In my example, say we have . As x approaches 0, the quotient approaches 1. You can get closer and closer to 1 when you chose an x closer and closer to 0. But it doesn't imply that if you chose 0 as x that you'll get 1 as the quotient! Be careful on this.