\[\large \lim_{x \to 0} \left( \frac{1}{x}\right )^{x} \]

Find the limit above if it exists.

**Notations**:

- \(e \approx 2.71828\) is the Euler's number.
- \(!\) denotes the factorial function. For example, \(8! = 1\times2\times3\times\cdots\times8 \).

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