The Limit of (1 - cos(x)) / 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 limit, you can vary the graph's bounds and consider an output-tolerance, ε, for the limit. The boundaries of this function, y = 2 / x and y = - 2 / x, are graphed in dashed-gray and a rectangle is also plotted with the entered ε-value (δ values for the definition of the limit are indicated on the graph, at the vertical edges of the rectangle -- they are not necessarily 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