# Shaped into a box

Calculus Level 5

Suppose we define a type of function $f\left( x \right) =\dfrac { k{ x }^{ n } }{ n+{ x }^{ n } }$ with $$n>0$$ and $$k>0$$. To calculate a convergent area above the curve for $$f\left( x \right)$$ over the domain of all real numbers, one can bound this area with a horizontal line, $$\displaystyle y=\lim _{ x\rightarrow \pm \infty }{ f\left( x \right) }$$.

Using this information, find an expression for this area as $$\displaystyle \lim _{ n\rightarrow \infty }{ f\left( x \right) }$$. Write your answer in terms of $$k$$.

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