Question

Evaluate the limit `lim_(h rarr 0) (1-cosh)/h^2` numerically ?

Answer 1

You cannot "prove" that a limit exists numerically but we can examine its general behaviour. The easiest way is to use a spreadsheet:

Define a function:

`F(h) = (1-cos h)/h^2`

Then we tabulate the function using and initial value of `h=1`and bisect the interval during each calculation:

As we can see with `h = 0.00000763` we have `f(h)=0.50000000`, but there still could be some odd behaviour or a discontinuity that we are unaware of in the interval:

`0 lt h lt 0.00000763`