# Perturbed function

1. Nov 19, 2009

### sprinkle

The Question that I have posted is attached due to the fact that the question could not be posted in this area.
I am very sorry for the inconvenience

Question is attached

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2. Nov 20, 2009

### HallsofIvy

Staff Emeritus
If you honestly care so little about this problem that you cannot take the time to type a couple of polynomials, why should anyone else care?

What you wrote was:
Consider the polynomial: f(x)= x^5- 300x^3- 126x+ 5005
which has a root alpha= 5. Also consider the perturbed function
F_e(x)= f(x)- epsilon x^5= (1- epsilon)x^5- 300x^3- 126x+ 5005
where epsilon is a small number. Letting alpha(epsilon) denote the perturbed root of F_e(x)= 0 corresponding to alpha(0)= 5, approximate alpha(epsilon)- 5.

There, that wasn't so hard, was it. I intentionally did not use html tags or LaTex in order to show that it could be written out easily. Many people will not open ".doc" files because they are notorious for harboring viruses.

As to your problem, replace x in the equation of F_e(x)= 0 by x= alpha- 5 and see what it reduces to.
corresponding to estimate

3. Nov 20, 2009

### sprinkle

HallsofIvy

thanks for that piece of info