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Why do we have limits? What is it's significanace in real life? why f(x) is arbitrary close to L for all x sufficiently close to a? How is limit of a function it's actual value? 

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we use limit to analyze where the function is going. for analogy, suppose you are sitting on a couch and start feeling thirsty so you start walking towards the fridge so in this instant if someone wants to describe where you are going, they would be confident to say that you are approaching the fridge because as time passes you are getting closer to the fridge. the limit works exactly like that it tells us where the function is going.

Analyzing a function is much more important than you realize in almost every field. 

The limit is just the first step of the Calculus. so the better way to put the question would be

why calculus is important?

and 

The most unhelpful, but most true answer: Basically everything.

Almost everything runs on, is modeled by, understood using calculus to some extent. Newton's second law, which is the basis of any kind of physical motion, and so used in all forms of engineering, mechanics, fluids, etc, etc, etc, is an equation in Calculus. The equations that allow us to discuss how electricity will flow, what magnetic fields will do, how the light will propagate, are Calculus equations. Even many things in something that may seem like it has nothing to do with Calculus benefit from it, or discrete versions of it, particularly in Computer Science.

Your whole world runs on Calculus. If you take advantage of anything invented after 1700, then you're more than likely directly benefiting from Calculus. Calculus is an infection. We are in symbiosis with Calculus.

Calculus tells us how things change, and everything changes, so we need Calculus for everything.

The thing with calculus is that its significance doesn't really sink in when you first learn about it. It takes a bit of time and usage to realize how useful a toolbox calculus is.

Posted by

Pankaj Sanodiya

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