calculus concretion found
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You can buy cheap air swimmers remote control flying clownfish and get them fast! The lyrics were actually written by my math professor, Dr. Sandra Keith. I am just performing it. The beat was made live using an MPC 1000 and a microkorg. The lyrics are as follows:
As hard as to find a good limit might be
It's just to say given e, find d
To get two curves to meet up is what we like
But they can't touch eachother only get real tight
Fit 'em in a window is our ambition
And we squeeze the window down like me and my tuition
So it's to produce the window that now comes next
eps with the y and delt with the x
eps stands for error which the boss will allow
Up and down from the limit on the y-axis-now
Don't forget, it's the error that you're given
Error my folks is the life of mathematicians
d stands for delta which you must find
It's "tolerance", and we need to keep it in mind
The error is a y-range, and it's a tiny bit
Then we find the x's that make the function fit
We gotta find the delta where the x can play
But we never do care that x hits "a"
A limit just means you get infinitely near
There's no such thing, so it oughtta be clear
You need a proof with words, take a general case
Get delta phrased in eps and then you win the race
To do a limit proof is always the worst
You write the definition down, gotta do that first
To write the definition is to make no mistake
The wording is crucial, man it takes the cake
First off, start and get yourself a pepsi
The next thing you say relates to epsi
"Given any eps must show there is a delt"
There's more to it than this, it's a rat you smelt
But given the proposal, now you're on your way
Get the two sides similar and then you say;
You can now take my delta framed in epsilonese
So the limit exists just as sure as you please
We can't really show things are infinitely close
So instead we meet the challenge that you post
As arbitrary as you want, the y's are neck to neck
As x approaches "a" but at "a" what the heck
And when does this fail, just what you now heard
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