The limit of $x \cdot e^{2 - x}$ as $x \to 2$ is $2$.

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Here are some related questions to deepen your understanding:

1. What is the derivative of the function $x \cdot e^{2 - x}$?
2. How would the limit change if the exponent were modified, such as $e^{3 - x}$?
3. Can this limit be evaluated using L'Hopital's Rule, and if so, how?
4. What happens to the function as $x \to \infty$?
5. How does this expression behave if we change the base of the exponent from $e$ to another constant?

Tip: When dealing with exponential functions, knowing their growth or decay rates helps in predicting limit behavior.