The Limit of sin(1/x) as x -> 0
by Mike Martin

On this page, you can visualize the limit of a function as the input goes to zero.   This page features the following limit

To investigate the supposed limit of zero, you can vary the graph's bounds and consider an output-tolerance, ε, for this supposed limit. The boundaries of this function, y = 1 and y = - 1, are graphed in dashed-gray and ε-bounds are plotted in dashed blue.   There are some ε bounds that correspond to existing δ bounds (indicated by a dashed blue box).   When δ bounds exist, they are not unique.   Use at your own risk as some parameter values may produce erroneous graphs, but parameters consistent with the literature will work.

Enter in the value of the limit's tolerance parameter ε and select the plotting bounds, then press the "Evaluate" button.



  ≤   x   ≤  


  ≤   f (x)   ≤  


ε =  


References:

To be added