If lim(x→∞) (5x² + 3x)/(2x² - x) = L, what is the value of L?

Core Concept

This is an indeterminate form ∞/∞. We can use L'Hôpital's Rule: lim(x→∞) (10x + 3)/(4x - 1). This is still ∞/∞, so apply L'Hôpital's Rule again: lim(x→∞) 10/4 = 5/2. Alternatively, divide numerator and denominator by the highest power of x (x²): lim(x→∞) (5 + 3/x)/(2 - 1/x) = 5/2.