All along all the path of an integral With a slope that's so constant, or flat, I was thinking I could model things that you might have Changing only the things that you had. You know I've always used some Euler (spent my life running code) And it's all linear change (you have to balance the load) But if you want to model behavior That's smooth as sand, still smoother, man, Here's what you do You just iterate the integral Halving the time step each time And take it to the limit one more time. You can spend all your time making changes You can spend all your change making time But if you need to find a derivative Here's all you do You just difference your function Then divide by the time And take it to the limit one more time. Take it to the limit, Take it to the limit, Just take it to the limit one more time. When you try to find a function's slope You may be stuck with zip over nil You may still find the local derivative With L'Hopital's Rule: You just form separate derivatives Of run and of rise And take it to the limit one more time. Take it to the limit, Take it to the limit, Just take it to the limit one more time. |