1. **State the problem:** We want to find the limit as $x$ approaches infinity of the function $$e^x - x^2.$$ 2. **Recall the behavior of the terms:** As $x \to \infty$, the exponential function $e^x$ grows much faster than any polynomial function like $x^2$. This means $e^x$ will dominate $x^2$ for very large $x$. 3. **Analyze the limit:** Since $e^x$ grows faster than $x^2$, the term $e^x - x^2$ behaves approximately like $e^x$ for very large $x$. 4. **Conclusion:** Therefore, $$\lim_{x \to \infty} (e^x - x^2) = \infty.$$ This means the function increases without bound as $x$ becomes very large.