Limit Definition of Derivative
limit (as h approaches 0)= F(x+h)-F(x)/h
The limit definition of derivative is a mathematical expression used to find the derivative of a function at a specific point. It is one of the fundamental concepts of calculus.
More specifically, let f(x) be a function, and let a be a real number. Then, the derivative of f(x) at x=a is given by the following limit:
f'(a) = lim_(h -> 0) [f(a+h) – f(a)] / h
where h is a small number (usually tending towards zero).
In other words, the limit definition of derivative tells us to find the slope of a tangent line to the curve of f(x) at point a by calculating the limit of the difference quotient as h approaches zero. The numerator of the above equation gives the change in f(x) over a small interval (a to a+h), while the denominator gives the length of the interval. As h becomes smaller and smaller, the fraction becomes closer to the instantaneous rate of change of f(x) at point a.
This definition may seem complicated, but it is essential for understanding the concept of derivatives and their applications in calculus.
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