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Post date: Sep 29, 2013 12:54:4 PM
PARA SINGS 12
ax2 + bx + c presents....
"Don't Stop With Riemann"
(*aka "Don't Stop Believin'", Journey)
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Official video: Unable to locate (Copyright pull?)
Live Band Performance: Vevo here
Source Lyrics video: YouTube Here
Karaoke version: YouTube Here
Glee Lyrics version: YouTube Here
Karaoke Glee Version: YouTube Here
***
Just approach from left,
Estimate is low, I guess.
We want the area underneath this curve.
Just approach from right,
Estimate is high, how trite.
We want the area underneath this curve.
(Instrumental)
(Glee option call out: "Riemann!")
A manner to approximate?
A summation to contemplate!
Every trial helps us to refine
It goes on and on and on and on...
{Refrain:}
Segments, added. Up or down along this curve
Their width we'll narrow, out of sight.
Limit's useful, telling us to stop and observe
Gives us answers which are right!
Working with unending sums,
Series is what this becomes.
Breaking vastness into discrete parts
We'll comprehend.
Some see now, some years hence,
Some may only grasp a sense!
But the learning never ends,
It goes on and on and on and on...
{Refrain:}
Segments, added. Up or down along this curve
Their width we'll narrow, out of sight.
Limit's useful, telling us to stop and observe
Gives us answers which are right!
(Instrumental)
Don't stop with Riemann,
Try some integration!
Limits, useful, ohhhhhhh.
Don't stop with Riemann,
Try some!
Limits, useful, ohhhhhhh!
(repeating option)
Graph pics from this site:
http://www2.seminolestate.edu/lvosbury/CalculusI_Folder/RiemannSumDemo.htm
Explore with your own sums here:
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