>>11576646>>11576662He's saying if he explains it to you, then you don't already have anything meaningful to say to answer his question.
He's not willing to waste his time explaining it to you, since it doesn't benefit him.
I'll waste a little time, since I just woke up from a good dream, so I'm feeling generous.
Imagine you want to calculate the value of e, as an example.
You know e is a number that, when you take e^x, and when you differentiate e^x, they are the same
More specifically d(e^x)/dx = e^x
You know you can find d(f(x))/dx using the difference quotient
Y = a^x
y + dy = a^(x+dx)
A^x + dy = a^(x+dx)
dy = (a^(x+dx) - a^x)
dy/d = (a^(x+dx) - a^x)/dx
dy/dx = a^x (a^dx -1)/dx
dy/dx = a^x by definition
so 1 = (a^dx - 1)/dx
dx = a^(dx) - 1
dx+1 = a^dx
(dx+1)^1/dx = a
as dx -> 0, a -> the value of e
Let swap some values around to make it easier
if n = 1/dx
as dx -> 0, n -> infinity
we can rewrite A=(1/n + 1) ^ n
If you are familiar with binomial theorem, you know you can expand this,
(1/n + 1)^n = (nC0) + (nC1)(1/n) + (nC2)(1/n^2) ... (nCn)(1/n^n)
We know that
(nCk)1/(n^k) = [1/(k!)][n*(n-1)*n-2)...(n-k+1)/(n^k))
We know the limit as n-> infinity of (nCk)(1/n^k) = 1/(k!)
Which we can use with our binomial expansion, to produce a taylor series:
e = sum from n=0 to infinity 1/n! = 1/0! + 1/1! + 1/2! + 1/3! .... so on
This is useful, because it gives you the ability to calculate e to arbitrary precision
You can use this taylor series for a bunch of other things, like sine or cosine; which is useful to have a polynomial to find the value of sine by solving a 3rd degree polynomial, if you don't have a calculator on hand; which for many centuries engineers didn't
