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 evaluate the left-hand limit and the right-hand limit as \( x \) approaches 0.

### Step 1: Find the Left-Hand Limit
We start by calculating the left-hand limit as \( x \) approaches 0 from the negative side, denoted as \( x \to 0^- \).

\[ \lim_{x \to 0^-} \frac{e^{\frac{1}{x}} - 1}{e^{\frac{1}{x}} + 1} \]
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