Question

Let f (x) be differentiable on the interval (0, ∞) such that f (1) = 1, and $\underset{t \rightarrow x}{lim} \frac{t^2 f(x)- x^2 f(t)}{t-x} = 1$ for each x > 0. Then f(x) is
$(a) \frac{1}{3x}+\frac{2x^2}{3}\\(b) \frac{-1}{3x}+\frac{4x^2}{3}\\(c) \frac{-1}{x}+\frac{2}{x^2}\\(d) \frac{1}{x}$

Answer 1

Answer:

A

Step-by-step explanation: