Can linear equations be hard?

Algebra Level 5

Given that

f(x)=x1f\left( x \right) =\left| \left| x \right| -1 \right| P0(x)=f(x){ P }_{ 0 }(x)=f(x) Pn+1(x)=f(Pn(x)){ P }_{ n+1 }(x)={ f(P }_{ n }(x))

Ak=limn0kPn(x)0.5dxA_{k}=\left| \lim _{ n\rightarrow \infty }{ \int _{ 0 }^{ k }{ { P }_{ n }(x) } -0.5dx } \right|


And that k0k_{0} is the minimum value such that A=Ak0A=A_{k_{0}}, where kk ranges over all the positive reals k>0k>0.

Find 1000(A+k0)\left\lfloor 1000(A+k_{0}) \right\rfloor

Try my Other Problems


Problem Loading...

Note Loading...

Set Loading...