1. **Problem statement:** Find the limit $$\lim_{x \to +\infty} \left(1 - \frac{3}{x}\right)^x$$. 2. **Recall the formula:** The limit $$\lim_{x \to \infty} \left(1 + \frac{a}{x}\right)^x = e^a$$ is a fundamental limit in calculus. 3. **Rewrite the expression:** Here, $$1 - \frac{3}{x} = 1 + \frac{-3}{x}$$, so $$a = -3$$. 4. **Apply the formula:** Using the formula, we get $$\lim_{x \to +\infty} \left(1 - \frac{3}{x}\right)^x = e^{-3}$$. 5. **Interpretation:** This means as $$x$$ becomes very large, the expression approaches $$e^{-3}$$, which is approximately 0.0498. **Final answer:** $$\boxed{e^{-3}}$$.