a) Define a function f(x)=sin(1/x). Plot graphs of f zooming in around 1/Pi, 1/1

Question

a) Define a function f(x)=sin(1/x). Plot graphs of f zooming in around 1/Pi, 1/10Pi, 1/200Pi. You should be able to zoom in close enough so that the function look nice and smooth.
b) Pick two numbers that are VERY close to 0 and plot f in a VERY small neighborhood. You should be able to zoom in close enough so that the function looks nice and smooth.
c) Try plotting graphs of f zooming in around 0. State three y-values that occur in your graph no matter how much you zoom in around 0. What does this say about the limit of f at 0?

I have to do this on maple software. Thank you

Explanation / Answer

You have to be careful about division by zero, especially with tikz. With pgfplots there are ways to handle such cases more elegantly. So, I have changed the domain slightly below to avoid this problem.I'd recommend using an extra pair of braces: So, instead of x*x I would recommend you get into the habit of (x)*(x). In this specific case it may not matter, but it does matter if you were to use x^2 which may yield incorrect results for negative values of x.

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