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f[x_]:=1–
2
(x–1)
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[nn_,kk_]:=Moduleint=Reduce<=f[x]<=&&0<=x<=2,x/.{n–>nn,k–>kk}/.{Or–>List}/.{Inequality–>List},If[int===False,Nothing,If[Length[int]==2,If[Head[int]===Equal,{int[[–1]],int[[–1]]},int[[;;,{–1,1}]]],int[[{1,–1}]]]]
k–1
n
2
k
n
2
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[nn_]:=Module[{int=Reduce[f[x]>=n&&x<=2,x]/.{n–>nn}/.{Or–>List}/.{Inequality–>List}},If[int===False,Nothing,If[Length[int]==2,If[Head[int]===Equal,{int[[–1]],int[[–1]]},int[[;;,{–1,1}]]],int[[{1,–1}]]]]]
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χ[n_,k_,x_]:=Module[{int=[n,k]},If[int===Nothing,0,If[Between[x,int],1,0]]]
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χ[n_,x_]:=Module[{int=[n]},If[int===Nothing,0,If[Between[x,int],1,0]]]
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ϕ[n_,x_]:=Sumχ[n,k,x]+nχ[n,x],{k,1,n*}
k–1
n
2
n
2
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ManipulateShowPlot[{1–,ϕ[n,x]},{x,0,2},Evaluated–>True,PlotPoints–>100,PlotTheme–>"Detailed"],NumberLinePlotInterval/@[n,#]&/@Range[n],Spacings–>Join{0},Table,,{n,1,5,1}
2
(x–1)
n
2
1
n
2
n
2
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ListAnimateTableShowPlot[{1–,ϕ[n,x]},{x,0,2},Evaluated–>True,PlotPoints–>100,PlotTheme–>"Detailed"],NumberLinePlotInterval/@[n,#]&/@Range[n],Spacings–>Join{0},Table,,{n,1,5,1}
2
(x–1)
n
2
1
n
2
n
2
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