Is there any other name for limits? 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.
Already checked on two questions here

The limit of a function to a particular value describes the behaviour of the function as the function value approaches that value. As an example the following
$\displaystyle \lim_{x\rightarrow x_{0}} f(x) = c \tag{1}$
implies that as $x$ approaches the value $x_{0}$ that the function $f(x)$ takes the value $c$. To demonstrate this we could say $f_{1}(x) = x + 2$, $x_{0} = 2$ and $c=4$ when $f_{1}(x)$ is a function on the real numbers. There are also situations when the limit does not exist. For example consider the function
$f_{2}(x) = \displaystyle \begin{cases} 1, \quad x \geq 0 \\ 0, \quad x < 0.\end{cases}$
Now how do we define the limit of this as $x\rightarrow 0$ i.e., what is $\lim_{x\rightarrow 0} f_{2}(x)$? The answer is that it doesn't exist, as depending on whether we approach $0$ from above or below we get different answers. To show this we introduce the notation $0_{\pm}$ to mean either the 'right' side of zero ($0_{+}$) or the 'left' side of zero ($0_{-}$).
Now we see that if we approach $x=0$ from the right, i.e.
$\displaystyle \lim_{x\downarrow 0_{+}} f_{2}(x) = 1$
but if we approach it from the left, i.e.
$\displaystyle \lim_{x\uparrow 0_{-}} f_{2}(x) = 0.$
The left hand limit does not equal the right hand limit, so the limit at zero is not well defined for $f_{2}$. This characterizations tells us that $f_{2}$ is a discontinuous function. In contrast $f_{1}(x) = x + 2$ is a continuous function as its left limit equals its right limit
