1. Let's start by stating the problem: How to solve equations involving limits as the variable approaches infinity. 2. The key formula is the definition of limit at infinity: $$\lim_{x \to \infty} f(x) = L$$ means as $x$ grows larger and larger, $f(x)$ approaches the value $L$. 3. Important rules: - If the degree of the numerator polynomial is less than the degree of the denominator, the limit is 0. - If degrees are equal, the limit is the ratio of leading coefficients. - If the numerator degree is greater, the limit is infinity or negative infinity depending on signs. 4. Example: Solve $$\lim_{x \to \infty} \frac{3x^2 + 5}{2x^2 - x + 1}$$ 5. Step 1: Identify degrees. Numerator degree = 2, denominator degree = 2. 6. Step 2: Since degrees are equal, limit is ratio of leading coefficients: $$\frac{3}{2}$$. 7. Therefore, $$\lim_{x \to \infty} \frac{3x^2 + 5}{2x^2 - x + 1} = \frac{3}{2}$$. 8. In plain language: When $x$ becomes very large, the lower degree terms become insignificant, so the function behaves like the ratio of the highest degree terms. This method applies to many rational functions and helps find limits at infinity easily.