I guess my original question was are these assertions correct independently, even if i didn't prove them?
Is this true?
\lim_{a\rightarrow 0} \frac{b}{a} = \lim_{d\rightarrow \infty} bd
1 = \lim_{y\rightarrow 0}\lim_{m \rightarrow \infty} my
Here is a different way I (think I) proved that the derivative of e^x is e^x:https://docs.google.com/document/edit?id=1_QqZaeDlQObgbTg3zd5ezlWuaUol92k7cBaOjdBzoSM&hl=en&authkey=CPuduaIB
Are my "rules" with infinitives correct or do they not work in other cases?