Oh, and another thing I wanted to point out is, I said that we had to know the binomial theorem. But if you think about it, we really didn't even have to know the binomial theorem. Because we knew in any binomial expansion, I mean, you'd have to know a little bit. But if you did a little experimentation, you would realize that whenever you expand a plus b to the nth power, the first term is going to be a to the n. And then the second term is going to be plus n a to the n minus 1 b. And then you could keep having a bunch of terms. But these are the only terms that are relevant in this proof, because all the other terms get canceled out when delta x approaches 0. So if you just knew that, you could have done this.