AP Calculus ABmediummcq1 pt
If lim(x→∞) (5x² + 3x)/(2x² - x) = L, what is the value of L?
A.0
B.5/2
C.2/5
D.∞
Explanation
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.
Correct Answer
B5/2
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