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Differentiation the limit on the graph

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.