1. **Problem:** Determine if the function $f(x)=x^3+x^2-2$ is continuous at $x=1$. 2. **Formula and rule:** A function is continuous at $x=a$ if $\lim_{x \to a} f(x) = f(a)$. 3. **Evaluate $f(1)$:** $$f(1) = 1^3 + 1^2 - 2 = 1 + 1 - 2 = 0$$ 4. **Evaluate the limit as $x \to 1$:** Since $f(x)$ is a polynomial, it is continuous everywhere, so $$\lim_{x \to 1} f(x) = f(1) = 0$$ 5. **Conclusion:** The function is continuous at $x=1$ because the limit equals the function value.