task3

function y = Degenerate_Fred_II_Taylor(K,f,a,b,lambda,power)
    [alpha, beta]=coeffs(taylor(K,'Order',power+1),x);
    for i = 1:length(alpha)
        s = char(alpha(i));
        s(1,1)='x';
        alpha(i)=s;
    end
    n=numel(alpha);
    A=zeros(n);
    for j=1:n
        A(:,j)= -lambda*int(beta*alpha(j),a,b);
        A(j,j)=1+A(j,j);
    end
    r=int(beta*f,a,b)';
    c=A\r;
    y=dot(c,alpha)*lambda+f;
end