JEE Main 2024 Mathematics question
Let f be a differentiable function in the interval (0, ∞) such that f(1) = 1 and for each x > 0. Then 2 f(2) + 3 f(3) is equal to .
Answer: 24
Solution
The limit equals 2x f(x) − x² f′(x) = 1, i.e. f′ − 2f/x = −1/x². With integrating factor x⁻²: (f/x²)′ = −x⁻⁴, so f/x²
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