Alternative form of the definition of the derivative
lim x->c. f(x)-f(c) / x-c
The derivative of a function f(x) at a point x=a can also be defined as the limit of the difference quotient as h approaches zero, where h is the change in x. That is:
f'(a) = lim[h -> 0] (f(a+h) – f(a))/h
This definition states that the derivative of a function at a point can be obtained by finding the limiting value of the slope of a secant line between two points on the curve as the distance between the two points approaches zero. It is an important alternative definition of the derivative and is used extensively in calculus.
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