Solution: Divide numerator and denominator by x^2. The limit becomes lim (x -> ∞) (2 + 3/x^2)/(5 - 4/x + 1/x^2) = 2/5.
Steps: 7
Step 1: Identify the limit you need to evaluate: lim (x -> ∞) (2x^2 + 3)/(5x^2 - 4x + 1).
Step 2: Notice that both the numerator and the denominator have terms with x^2. To simplify, divide every term in the numerator and the denominator by x^2.
Step 3: Rewrite the limit after dividing: (2x^2/x^2 + 3/x^2)/(5x^2/x^2 - 4x/x^2 + 1/x^2).
