This makes each term in the sequence y(x). It is also trivial that y(x) = eln(y(x)), which, in this case, is easier to study. He made use of the logarithm rule: ln(ax) = xln(a), and algebra: x = 1/(1/x), provided x is not 0.I am having trouble with why he choose to let y what it does and how we went on from there.
How did he get
The second limit gives us the indeterminate form 0/0, which makes it valid to use L'Hôpital's rule. This was the point of writing x as 1/(1/x).How did he arrive at the 2x^2 / (x+3)(x+1) step? Is there something I'm missing he did when he took the limit to infinity?