# Mixing of concepts!

Calculus Level 5

A function is defined as $$f(x)=ax^4+bx^3+cx^2+dx+\lambda$$. This function has a special property: $$\dfrac{f(1)}{1}=\dfrac{f(2)}{2}=\dfrac{f(3)}{3}$$. If $$\displaystyle \lim _{ x\to \infty }{ \dfrac { f( x ) }{ { x }^{ 4 } } } =1$$, then find $$f(i)+f(-i)$$ where $$i=\sqrt{-1}$$.

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