Differentiation as a limit
Choose or change the function f(x) and choose starting point where x = a
set n=0 (or just big enough to see the whole of the chord AB
h is "a little bit more" so that we are looking at A (x=a, y= f(a)) and B, a bit further up the curve (x=a+h, y= f(a+h))
So the line AB i a first approximation of the tangent to f(x) at A.
As h gets smaller and smaller the gradient of line AB gets closer and closer to the gradient of the tangent at A.
(in this applet h gets smaller as n gets bigger : h=1/)
The diagram explains how limits are used to understand differentiation from an analytical point of view.