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

When a mathematician says the "limit of $f(x)$ is $L$ (as $x$ approaches some number $c$)", he/she means something quite complex.  He/she means that when some $x$-values that are close to $c$ (but not actually $x=c$) are plugged into $f(x)$, then the values of $f(x)$ are close to $L$.  For example, we feel confident that $\displaystyle{\lim_{x \to 3} x^2 = 9}$ because $(2.99)^2 = 8.9401$, and $(2.9999)^2 = 8.9994$, and $(3.0000001)^2 = 9.0000006$.  In each of these calculations, I plug in a number close to $x=3$ and expect the result to be close to $y=9$.  Roughly speaking, the word "limit" refers to the ultimate end result of the process of plugging in numbers $x$ that are closer and closer to the target.
But why can't you just plug in $x=3$ into $x^2$ to find out $(3)^2 = 9$, I bet you're wondering.  Yes, in this case we can, because $y=x^2$ is nice and continuous, but not all functions are quite so nice.  We may also want to examine what are the values of $f(x) = \frac{\sin x}{x}$ near $x=0$.  In that case, plugging in $x=0$ does no good, so we go the long way around; plug in numbers that are close to $x=0$ (but not equal to $0$).
$$
\begin{align*}
  x = 0.1 &\Rightarrow \frac{\sin 0.1}{0.1} \approx 0.9983341665\\
  x = 0.01 &\Rightarrow \frac{\sin 0.01}{0.01} \approx 0.9999833334\\ 
  x = 0.001 &\Rightarrow \frac{\sin 0.001}{0.001} \approx 0.9999998333\\ 
\vdots & 
\end{align*}
$$
After some consideration and calculations, we feel confident that there is some end result, some limiting value to which these numbers approach, a limit to be brief, and that value seems to be $y=1$.  (ok, technically, this just gives us evidence that the limit (as $x=0$ is approached from the right) is probably very close to $1$).
The $\epsilon$-$\delta$ approach is a way to make the process rigorous.  What does it really mean to approach a value closer and closer  How close is close enough?  I would encourage you to get a good conceptual grasp on how limits work before tackling the $\epsilon$'s and $\delta$'s.
Hope this Helps!
