1. The problem is to find the limit of a function as the variable approaches infinity. 2. The general idea is to analyze the behavior of the function when the input grows very large (approaches $\infty$). 3. Common rules: - If the function is a rational function (ratio of polynomials), compare the degrees of numerator and denominator. - If the degree of numerator $>$ degree of denominator, limit is $\infty$ or $-\infty$ depending on signs. - If degrees are equal, limit is ratio of leading coefficients. - If degree of numerator $<$ degree of denominator, limit is 0. 4. For other functions like exponentials, logarithms, or trigonometric functions, use known limits or apply L'Hôpital's rule if the limit is indeterminate. 5. Example: Find $\lim_{x \to \infty} \frac{3x^2 + 5}{2x^2 - x + 1}$. 6. Since numerator and denominator are degree 2, limit is ratio of leading coefficients: $$\lim_{x \to \infty} \frac{3x^2 + 5}{2x^2 - x + 1} = \frac{3}{2}$$ 7. If you have a specific function, please provide it for a detailed solution.