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f:=.1*x^4+.1*x^3+.2*x^2+(.25-1)*x+.35;}
fsolve(f,x,0..1);


             Exercises/Experiments
2.
x:=(p+q/2)^2;
y:=2*(p+q/2)*((1-p-q)+q/2);
z:=1-x-y;
X:=(x+y/2)^2;
simplify(X-x);

3c.
for part(a):

u:=(2*pA*pa)^2*(1/4)+2*(2*pA*pa)*pa^2*(1/2)+(pa^2)^2;
pA:=1-pa;
aaxaa:= pa->(pa^2)^2/u;
# similarly for AaxAa and Aaxaa

for part(b):
plot(aaxaa,pa=0.001..0.25);

for part(c):
eval(AaxAa(0.01));

4d.
with(LinearAlgebra):
T:=Matrix([0,1],[1/2,1/2]);
v:=Vector([1/10,3/10]);
# the next to see the trend
for n from 0 to 10 do
   evalf((T^n).v);
od;
# Now get the eigenvalue and eigenvector
Eigenvectors(T);

6.
restart;
# First try
F:=x-> c*x+(1-c)*p^2;
x:=0; y:=F(x); w:=F(y);
simplify(%);
restart;
F:=x-> c*x+(1-c)*p^2;
y[0]:=0;
for n from 1 to 10 do
   y[n]:=F(y[n-1]):
od:
simplify(y[10]);