1. We are asked to find the limit: $$\lim_{x \to +\infty} \left(1 - \frac{3}{x}\right)^x$$ 2. This is a classic limit of the form $$\lim_{x \to \infty} \left(1 + \frac{a}{x}\right)^x = e^a$$ where $a$ is a constant. 3. Here, $a = -3$, so we can rewrite the limit as: $$\lim_{x \to +\infty} \left(1 - \frac{3}{x}\right)^x = e^{-3}$$ 4. Explanation: As $x$ becomes very large, the term $\frac{3}{x}$ approaches 0, so the expression inside the parentheses approaches 1. The exponent $x$ grows without bound, and the expression approaches the exponential function $e$ raised to the power of the constant $a$. 5. Therefore, the limit is: $$\boxed{e^{-3}}$$