Physical meaning of limit

Question

Does the concept of "limit" have a well-defined physical meaning (like, for example, the derivative)?

Answer 1

As Alan said, there is a rigorous mathematical $\epsilon - \delta $ definition, but I'm not sure that's exactly what you're after. It really depends on what you mean by a 'physical' definition.

I suppose it can be made less abstract by saying that, given a function $f(x)$, it can be made arbitrarily close to it's limit $L$ (to within $\epsilon $) at a point P by making $x$ sufficiently close enough to $p$ (to within $ \delta $). But I think there is no familiar 'real world' interpretation like there can be with the derivative, integration, etc.

Answer 2

Ya there is, by using epsilon-delta definition

'our distance from C such that if x is within delta of C, then f of x is going to be within epsilon of L. If we can find a delta for any epsilon, then we can say that this is indeed. the limit of f of x as x approaches C.'

Answer 3

According to my acknowledge, it has not a physical meaning like the derivative. It is used to be viewed as a tool in calculus. Many concepts, such as "continuous", "derivate", " integral", is based on this concept.

May it helps...

Answer 4

It does have a (kind of) physical picture:

Microscopic: The derivative of a function is the limit of what you get by looking at it under a microscope of higher and higher power. ^[1]