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1. Orb := proc(f, x, x0, K1, K2) local x1, i, L; 
x1 := x0; 
for i to K1 do 
x1 := subs(x = x1, f);
end do; 
L := [x1]; 
for i from K1 to K2 do 
x1 := subs(x = x1, f); 
L := [op(L), x1]; 
end do; 
L; 
end proc;


        Orb(f, x, 0.4, 1000, 2000);


I. Stable points x = 0.5
Ii. stable points x = 0.6
Iii. stable points x =0.558, 0.765
Iv.  stable points  x = 1.236
v.  stable points x = 0.791
Vi.  stable points x = 0.735


FP := proc(f, x) 
evalf([solve(f = x)]); 
end proc
SFP := proc(f, x) local L, i, f1, pt, Ls; L := FP(f, x); Ls := []; f1 := diff(f, x); for i to nops(L) do pt := L[i]; if abs(subs(x = pt, f1)) < 1 then Ls := [op(Ls), pt]; end if; end do; Ls; end proc


SFP(2*x*(1 - x), x)
I. 0.5
Ii. 0.6
Iii. []
Iv. 1.236
V. 0.791
Vi. 0.735


2. C(1,2): Orb = 0.618, SFP = 0.618
C(2,3): Orb = 0.732, SFP = 0.732
C(12,17): Orb = 0.718, SFP = 0.718


3. Orb(2*x*(1 - x), x, 0.4, 0, 200) = 0.4,0.48,0.4992,0.49999872,0.5000000000,0.5000000000,...


        X = 0 always has values changing on it when the recurrence starts and the equation 
does not get stable until later iterations of the recurrence. In this equation, the bifurcation 
point is at x = 4.


4. Orb(2*x*(1 - x), x, 0.5, 0, 6)