Can a genius solve this please?

[hannah.ek94]

Question: The iteration form Xn+1=g(Xn), n=0,1,2.., is used to find the root x=λ of the equation f(x)=0, prove that if. Prove that if: g(x)= x-Q1(x)*f(x)-Q2(X)*(f(x))^2 –Q3(x)*(f(x))^3 And the derivatives of g and f exist , then (g(x)) is of order two if (1-Q1(x)*df/dx.

I'm totaly confused on this example given by my lecturer without any further explanation. I really appreciate it if someone can have a go at it. Thanks

 

[Ishuda]

Question: The iteration form Xn+1=g(Xn), n=0,1,2.., is used to find the root x=λ of the equation f(x)=0, prove that if. Prove that if: g(x)= x-Q1(x)*f(x)-Q2(X)*(f(x))^2 –Q3(x)*(f(x))^3 And the derivatives of g and f exist , then (g(x)) is of order two if (1-Q1(x)*df/dx.

I'm totaly confused on this example given by my lecturer without any further explanation. I really appreciate it if someone can have a go at it. Thanks

You seem to have stopped in the middle of the problem. That is 'if (1-Q1(x)*df/dx' what?

 

[hannah.ek94]

You seem to have stopped in the middle of the problem. That is 'if (1-Q1(x)*df/dx' what?

Sorry about that, i have given the rest of the problem in a new sentence but i mistakenly put a full stop in there. here it is anyways:
The iteration form Xn+1 =g(Xn) , n=0,1,2,… is used to find the root x=λ of the equation f(x)=0,
Prove that if g(x)=x-Q1(x) *f (x)-Q2(X) * (f(x))^2 –Q3(x)*(f(x))^3 and the derivatives of g and f exist, then (g(x)) is of order of two if (1-Q1(x)*df/dx (x) =0

Sorry i study in Iraq (Kurdistan) so i dont know to what extend this is similar to what everyone else studies on a mathematics degree. Thanks in advance!

 

[Ishuda]

Sorry about that, i have given the rest of the problem in a new sentence but i mistakenly put a full stop in there. here it is anyways:
The iteration form Xn+1 =g(Xn) , n=0,1,2,… is used to find the root x=λ of the equation f(x)=0,
Prove that if g(x)=x-Q1(x) *f (x)-Q2(X) * (f(x))^2 –Q3(x)*(f(x))^3 and the derivatives of g and f exist, then (g(x)) is of order of two if (1-Q1(x)*df/dx (x) =0

Sorry i study in Iraq (Kurdistan) so i dont know to what extend this is similar to what everyone else studies on a mathematics degree. Thanks in advance!

Look at the derivative of g for f(x)=0.