- #1
AakashPandita
- 157
- 0
is it that limit can be taken for something approaching to any value while derivative is limit for the value of that thing approaching to zero?
A limit is a mathematical concept that describes the behavior of a function as its input approaches a certain value. It represents the value that the function approaches, but may not necessarily reach. A derivative, on the other hand, is the instantaneous rate of change of a function at a specific point. It represents the slope of the tangent line to the function at that point.
Limits and derivatives are closely related concepts. In fact, the derivative of a function at a specific point can be found by taking the limit of the function as the distance between two points approaches zero. This is known as the limit definition of a derivative.
Limits and derivatives have many practical applications in various fields such as physics, engineering, and economics. They are used to determine rates of change, optimization, and to model real-world phenomena.
Yes, it is possible for a function to have a limit but not a derivative. This can occur when the function is not continuous at the point in question, meaning that there is a gap or break in the graph of the function at that point.
Limits and derivatives are used to find the maximum and minimum values of a function by finding the points where the derivative is equal to zero. These points, known as critical points, can be used to determine whether a function has a maximum or minimum value at that point. By comparing the values of the function at these critical points, the maximum and minimum values of the function can be determined.