Wednesday, May 7, 2014

A fascinating example of the seeming advantages, and catastrophic unintended consequences of changing the formal definition of a derivative from $f'(x) = \lim_{h \rightarrow 0} \frac{f(x+h) - f(x)}{h},$ to $f'(x) = \lim_{h \rightarrow 0} \frac{f(x+h) - f(x-h)}{2h}.$