If f(x) is a differentiable function in the interval (0, ∞) such that f(1)=1 and lim_t → x (t^2 f(x)-x^2 f(t))/(t-x)=1, for each x>0, then f(3/2) is…

If $\displaystyle f(x)$ is a differentiable function in the interval $\displaystyle (0, \infty)$ such that $\displaystyle f(1)=1$ and $\displaystyle \lim _{t \rightarrow x} \frac{t^2 f(x)-x^2 f(t)}{t-x}=1$, for each $\displaystyle x>0$, then $\displaystyle f\left(\frac{3}{2}\right)$ is equal to: