I'm still working with a function represented by the blue function in pic. (sin squared of pi x over sin squared of pi x over k)
Anyway, when you break it apart and look at a location where x is a multiple of k, in the pic k is 5, you see it's a 0/0 form if you leave the one sin squared on the bottom, or you could think of it as 0 times infinity if you bring it to top as csc squared.
However, there's some limit, or it converges to k squared, see next pic.
So where is that coming from?
Somehow the one function dominates the other, and if you look at the limit using derivatives, it starts this whole chain of functions that gets out of hand rapidly.
Is there a way to show this easily? or do you have to track all those functions and show that they all cancel somehow leaving a remainder?
Anyway, when you break it apart and look at a location where x is a multiple of k, in the pic k is 5, you see it's a 0/0 form if you leave the one sin squared on the bottom, or you could think of it as 0 times infinity if you bring it to top as csc squared.
However, there's some limit, or it converges to k squared, see next pic.
So where is that coming from?
Somehow the one function dominates the other, and if you look at the limit using derivatives, it starts this whole chain of functions that gets out of hand rapidly.
Is there a way to show this easily? or do you have to track all those functions and show that they all cancel somehow leaving a remainder?
