> #sfb Oct 2, 2001
> f:=x^3-2*x+5;plot(f,x=-3..3);#f:=x^3-2*x+5
> solve(f,x);exact:=solve(f,x)[1];evalf(exact);
> approx:=evalf(solve(f,x));fsolve(f);
> for i from 1 to 10 do expand((x+y)^i) od;
> # Section 8.3 Work -- Force through Distance 
> #
> # Prob Densities and Cumulative distributions
> f:=exp(-(x-mu)^2/(2*sigma^2))/(sigma*sqrt(2*Pi));
> fm5s1:=subs({mu=5,sigma=1},f);fm5s2:=subs({mu=5,sigma=2},f);fm5s3:=subs({mu=5,sigma=3},f);
> fm4s1:=subs({mu=4,sigma=1},f);fm6s1:=subs({mu=6,sigma=1},f);
> plot([fm5s1,fm5s2,fm5s3],x=0..10,legend=["sigma=1","sigma=2","sigma=3"]);
> plot([fm4s1,fm5s1,fm6s1],x=0..10,legend=["mu=4","mu=5","mu=6"]);
> int(fm5s1,x=-infinity..infinity);
> int(fm5s2,x=-infinity..infinity);
> int(fm5s3,x=-infinity..infinity);
> int(f,x=-infinity..infinity);
> t1:=subs({mu=72.24,sigma=12.387},f);
> Bell:=plot(t1,x=40..100):Bell2:=plot(t1,x=70..80,filled=true,color=red):
> with(plots);display(Bell,Bell2);
> histogram:=[[40+5,1/250],[50+5,4/250],[60+5,5/250],[70+5,7/250],[80+5,5/250],[90+5,3/250]];
> Hist:=plot(histogram,x=40..100):Hist;
> display(Bell,Hist);
> h:=piecewise(x<40,0,x<50,1,x<60,4,x<70,5,x<80,7,x<90,5,x<100,3,0);
> plot(h,x=40..100);
> Bell3:=plot(h/250,x=40..100):display(Bell,Bell3);
> int(h/250,x);
> Dis:=plot(1+int(h/250,x),x=40..100):
> int(t1,x);
> Dis2:=plot(0.5+int(t1,x),x=40..100):
> display(Dis,Dis2);
> int(exp(-x^2),x=-infinity..infinity);
> #The problem from test2 -- time (x) x is in seconds
> rho:=lambda*exp(-lambda*x);
> rho:=piecewise(x<0,0,lambda*exp(-lambda*x));
> int(rho,x=-infinity..infinity);
> lambda:=1/100;int(rho,x=-infinity..infinity);
> plot(rho,x=-20..200,title="The way electronics wears out");
> failuresInFirstThreeSeconds:=int(rho,x=0..3);evalf(failuresInFirstThreeSeconds);
> xbar:=int(x*rho,x=-infinity..infinity);
> eqn:=int(rho,x=-infinity..T)=0.99;
> solve(eqn);
> solve(eqn)/60.0;
>