clear
x = linspace(-5,5);
f = inline('1./(1+x.^2)');
y = f(x);
plot(x,y), grid on, axis([-5 5 -1 2])
pause
X = [-5 0 5];
Y = f(X);
a = polyfit(X,Y,2);
p = polyval(a,x);
plot(x,y,x,p,X,Y,'o'), grid on, axis([-5 5 -1 2])
pause
X = [-5 -2.5 0 2.5 5];
Y = f(X);
a = polyfit(X,Y,4);
p = polyval(a,x);
plot(x,y,x,p,X,Y,'o'), grid on, axis([-5 5 -1 2])
pause
X = -5: 5;
Y = f(X);
a = polyfit(X,Y,10);
p = polyval(a,x);
plot(x,y,x,p,X,Y,'o'), grid on, axis([-5 5 -1 2])
pause
T = ((0:10)*2+1)*pi/22;
X = 5*cos(T);
Y = f(X);
a = polyfit(X,Y,10);
p = polyval(a,x);
plot(x,y,x,p,X,Y,'o'), grid on, axis([-5 5 -1 2])