CLOSE TO WOLFRAM

From: Norman Albers <nvalbers@gmail.com>
Date: Sat, 8 Jul 2017 09:31:20 -0700
Subject: kewlness
To: Steven Albers <scalbers@webtv.net>

Here is a nice little meditation on limits, of which I had wondered.
This Wolfram expression is the cat’s meow. I would have come close
with this reasoning:
Seeking INT sqrt[ r/(r-1) ] dr, IN THE FAR, hmmmmmm:
INT sqrt[1/(1-1/r) ]dr which may be approximated,
.. sqrt [1+1/r ] dr and thus by a far limit
of: r + 1/2log r, whoa, kewlness reigns.
Toadily, cuz I need to know when I may use such handy-dandy tools.
For those versed in algebra and math, this sez sure you get the ‘r’ term you should, and also, TO NEXT ORDER, WHEN ANALYZED IN THE FAR, meaning that r >>1.

There is a third order term when we analyze IN THE FAR. Look at the first term in the solution: √ [ r(r-1) ] . Expand this for “large ‘r’, hah, ’tis a surprising little exercise. IN SUM, THE RESULT VERY FAR AWAY, FOR LARGE ‘r’ , IS:
‘r’, + 1/2 log (r) + 1/2           !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!