Differentiation as a limit[br][br]Choose or change the function f(x) and choose starting point where x = a[br]set n=0 (or just big enough to see the whole of the chord AB[br][br]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))[br][br]So the line AB i a first approximation of the tangent to f(x) at A.[br]As h gets smaller and smaller the gradient of line AB gets closer and closer to the gradient of the tangent at A.[br](in this applet h gets smaller as n gets bigger : h=1/[math]2^n[/math])[br][br]The diagram explains how limits are used to understand differentiation from an analytical point of view.