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Let f (x) be a diffentiable function in ...

Let `f (x)` be a diffentiable function in `[-1,oo) and f (0) =1` such that `Lim _(t to x +1) (t^(2) f(x+1) -(x+1) ^(2) f(t))/(f (t) -f(x+1))=1.` Find the value of `Lim _(x to 1) (ln (f(x )) -ln 2)/(x-1)` .

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