Let $f:(0, \infty) \rightarrow(0, \infty)$ be a dif ferentiable function such that $f(1)=e$ and $\lim _{t \rightarrow x} \frac{t^2 f^2(x)-x^2 f^2(t)}{t-x}=0$ If $f(x)=1$, then $x$ is equal to :
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