JEE Main 2024 Mathematics question
For a, b > 0, let be a continuous function at x = 0. Then is equal to:
Answer: (D)
Solution
Left limit = (a + 1) + b = 3, so a + b = 2. Right limit: √(ax + b²x²) − √(ax) ≈ b²x²/(2√(ax)), so the limit is b/(2a) = 3 and b/a = 6.