JEE Main 2024 Mathematics question
Let be differentiable in (−∞, 0) ∪ (0, ∞) and f(1) = 1. Then the value of e a, such that f(a) = 0, is equal to .
Answer: 2
Solution
Since f(r)² − f(x)f(r) = f(r)(f(r) − f(x)), the limit is x f(x) f′(x), so [f(x)]² = x f(x) f′(x) − x³. Put y = f(x) = tx: t²x² = t x²(t + x dt/dx) − x³eᵗ, which
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