1. **Problem:** Find the limit of the function $f(x) = x^2 + x - 3$ as $x \to 0$. 2. **Formula and rules:** The limit of a polynomial function as $x$ approaches a value is simply the value of the polynomial at that point because polynomials are continuous everywhere. 3. **Intermediate work:** $$\lim_{x \to 0} (x^2 + x - 3) = 0^2 + 0 - 3 = -3$$ 4. **Explanation:** Since the function is a polynomial, we can directly substitute $x=0$ to find the limit. **Final answer:** $$\boxed{-3}$$