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Let nnn be a positive nonzero integer and
k=4n,k=4n,k=4n, a=x+x2−k2,a=x+\sqrt { { x }^{ 2 }-{ k }^{ 2 } }, a=x+x2−k2, b=x−x2−k2,b=x-\sqrt { { x }^{ 2 }-{ k }^{ 2 } }, b=x−x2−k2, f(x)=121kk(ak+bk).f\left( x \right) =\dfrac { 1 }{ 2 } \dfrac { 1 }{ { k }^{\displaystyle k } } \left( { a }^{ \displaystyle k }+{ b }^{\displaystyle k } \right).f(x)=21kk1(ak+bk).
For what integer n<1000n<1000n<1000 does f(x)f\left( x \right) f(x) intersect cos(x)\cos\left( x \right) cos(x) the most times between −4π<x<4π-4\pi <x<4\pi −4π<x<4π?
You may want to use a graphing calculator.
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