Evaluate the given limits using the graph of the function $f(x) = \displaystyle \frac{1}{e^x + 1}$ shown above.

1. $\displaystyle \lim_{x \to -\infty} f(x)$ =
2. $\displaystyle \lim_{x \to \infty} f(x)$ =
3. $\displaystyle \lim_{x \to 0^-} f(x)$ =
4. $\displaystyle \lim_{x \to 0^+} f(x)$ =
5. $\displaystyle \lim_{x \to 0} f(x)$ =

See limit