finding increasing period of f(x) = Sin(b/x)

[jwpaine]

I know that the period of f(x) = Sin(x/b) would 2(pi)b But how would I find the increasing period of this, (from what I can conclude by looking at its graph) this non-periodic function: f(x) = Sin(b/x)

What expression could I write for this increase in period? It almost looks exponential.

Thanks!

Looks like a vertical asympotote at x=0

 

[pka]

I know that the period of f(x) = Sin(x/b) would 2(pi)b But how would I find the increasing period of this, (from what I can conclude by looking at its graph) this non-periodic function: f(x) = Sin(b/x)Looks like a vertical asymptote at x=0

If you want a something like vertical asymptote graph \(\displaystyle \frac{{\sin (1/x)}}{x}\). The function \(\displaystyle \sin \left( {\frac{1}{x}} \right)\) has a huge history and is commonly called the topologist’s sine curve. You are absolutely correct to note that it is not periodic.

 

[jwpaine]

Thanks Pka.

From what I can find, "topologist’s sine curve" is far beyond what I have studied in-class.

I will look forward to better understanding this down the road.