1. The problem is to find the limit: $$\lim_{x \to +\infty} \frac{e^x}{x^{100}}$$. 2. We use the fact that exponential functions grow faster than any polynomial function as $x$ approaches infinity. 3. More formally, for any positive integer $n$, $$\lim_{x \to +\infty} \frac{e^x}{x^n} = +\infty$$. 4. Here, $n=100$, so the limit is $$+\infty$$. 5. This means that as $x$ becomes very large, $e^x$ grows much faster than $x^{100}$, so the fraction increases without bound. Final answer: $$\lim_{x \to +\infty} \frac{e^x}{x^{100}} = +\infty$$.