Limit Definition of Derivative
limit (as h approaches 0)= F(x+h)-F(x)/h
The limit definition of derivative is a mathematical formula that is used to calculate the derivative of a function at a particular point. The derivative of a function is the rate of change of the function at a particular point. The limit definition of derivative is defined using the concept of limit.
Suppose we have a function f(x). The derivative of the function f(x) at a particular point x=a is denoted by f'(a) and is defined as:
f'(a) = lim (h->0) [f(a+h) – f(a)]/h
Here, h is the distance between x and a. As h approaches zero, the formula computes the slope of the function at x=a. The slope of the function at x=a is also known as the tangent line slope at x=a.
The limit definition of derivative is an important tool used in calculus to solve a wide range of problems. It helps to calculate the instantaneous rate of change of a function at a particular point.
Although the limit definition of derivative can be computationally intensive, it is a fundamental concept in calculus and helps in understanding more complex concepts in calculus such as integration and differentiation.
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