lim(n->0 +/- 0)(1/(1+e^(1/n)))

I think this is the limit you're asking for:

$\displaystyle\lim_{n\to \pm0} \frac{1}{1+e^{(1/n)}}$

This means the limit of the function as it approaches from the left of n=0 and the right of n=0

To find either, you need to find the value of $\frac{1}{1+e^{(1/n)}}$ when it approaches n=0 from the left or right hand side. The simplest way to do that is to calculate the values of the function at some very small positive n and some very small negative n (e.g. 0.0001 and -0.0001)

so when are you not allowed to this? or can you always do stuff like this (the taking a value close to it)?
I had no idea of this.

Completely ignore the above post, it's essentially attempting to guess, rather than actually proving anything. Use the definition of limits, and any sum, product, quotient and power rules you may have.

you know the thing is that I've never cone across these rules in my lectures or my lecture notes. I have heard of them in combinatorics though but that's the only thing. I guess I'll just search them up.

Posted from TSR Mobile

You may have heard of them under the name "algebra of limits".

Completely ignore the above post, it's essentially attempting to guess, rather than actually proving anything. Use the definition of limits, and any sum, product, quotient and power rules you may have.

Given how ambiguous the first post of this thread is, I don't think I'm at fault entirely here. Besides, I said "simplest" for a reason; it is a very simple way of doing it that provides and example of what is meant by the limit notation. In this case it just so happens to be accurate to several thousand decimal places of the correct answer for the right and left hand limit.