# 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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