Let f(x) be a continuously differentiable function on the interval (0, ) such that f(1) = 2 and _ t x t^ 10 f(x) - x^ 10 f(t) t^9 - x^9 = 1 for each x > 0. Then, for all x > 0, f(x) is equal to

JEE Advanced 2024 Mathematics question

Let be a continuously differentiable function on the interval such that and

= 1

for each . Then, for all , is equal to

Answer: (B)

The limit is of the form ; by L'Hôpital's rule in : , i.e. , or . Integrating factor : $' =

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Question ID VK-034164