I am in a total delusion about understanding limits relationg to real world elements. I am going the lecture notes again and again. So here Just not only I don't get delta epsilon approach it confuses me more.
- What is a limit?
- On what basis it is called a limit? Is there a better word to describe it? Is it called limit because it is limiting something that has impact on another? Such as $f (x)$ is a function of $x$. Now $x$ has a domain it could move around to make sure that $f (x)$ will exist? If $x$ doesn't comply with the domain then $f (x)$ will not exist? That means $f (x)$ is the limit and $x$ makes it to exist or not. Is that correct?
All I understand is that $x$ has forbidden values which shouldnt be plugged into certain functions of $x$. But since we are curious we want to know the last $x$ value before x hits the forbidden city. If that last point can make function of x to exist without going to infinity then can I say at this last point, the function exists? Why does it call limit I still don't get it. Is it because it is limiting x from making a mess in function of x?
Why do we need to find limits?
When obviously $x=-2$, function of $x$ $1/(x+2)$ is not going to be "okay". It will go to infinity, so can it be marked as not defined and $f(x)$ doesn't exist at $x=-2$? Should we just leave it like that or do we need to find "aid" that will not result in infinity?
Please have some mercy as I am really struggling to get the concept of limits right and stable.