A calculus problem - 2

Calculus Level 3

If \(f(x)\) is a polynomial satisfying \(\displaystyle \lim _{ x\to \infty }{ \dfrac { xf(x) }{ { x }^{ 5 }+1 } } =1\), \(f(1)=1\), \( f(2)=2\), \(f(3)=3\) and \(f(4)=4\) then what is \(\displaystyle \lim _{ x\to3 }{ \frac { x-f(x) }{ x-3 } } \)?

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