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// The equation cos(x)-x*%e^x==0 has real roots.
// the graph of this function can be observed here.
xset('window',8);
x=-1:.001:2; // defining the range of x.
deff('[y]=f(x)','y=cos(x)-x*%e^x'); //defining the cunction.
deff('[y]=fp(x)','y=-sin(x)-x*%e^x-%e^x');
deff('[y]=fpp(x)','y=-cos(x)-x*%e^x-2*%e^x');
y=feval(x,f);
a=gca();
a.y_location = "origin";
a.x_location = "origin";
plot(x,y) // instruction to plot the graph
title(' y = cos(x)-x*%e^x')
// from the above plot we can infre that the function has root between
// the interval (0,1)
// a=0;b=1,
// solution by chebyshev with a permissible error of 10^-15.
// we call a user-defined function 'chebyshev' so as to find the approximate
// root of the equation within the defined permissible error limit.
chebyshev(1,f,fp)
// hence the approximate root witin the permissible error of 10^-15 is
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