Show that `lim_(xto0^(-)) ((e^(1//x)-1)/(e^(1//x)+1))` does not exist.

Explanation

To show that the limit \( \lim_{x \to 0^-} \frac{e^{\frac{1}{x}} - 1}{e^{\frac{1}{x}} + 1} \) does not exist, we will analyze the behavior of the function as \( x \) approaches 0 from the left (negative side) and from the right (positive side).

### Step 1: Evaluate the limit as \( x \to 0^+ \)

Let \( x = h \) where \( h \to 0^+ \). Then we can rewrite the limit:

\[
\lim_{h \to 0^+} \frac{e^{\frac{1}{h}} - 1}{e^{\frac{1}{h}} + 1}
...