Evaluate the exponent of the exponential function as x approaches -infinity.

Let $u = \frac{1}{x}$.
As $x \to -\infty$, the value of $\frac{1}{x}$ approaches 0. Specifically, since $x$ is negative, $\frac{1}{x}$ approaches 0 from the negative side ($0^-$).

The original limit can be rewritten in terms of $u$:

The exponential function $e^u$ is continuous everywhere. Therefore, we can directly substitute the limit value into the function.

The final answer is $\mathbf{1}$.