having a little trouble with newton's method.

sin x = x^2; x>0

i found the equation after newtons to be:

x-sin x-x^2 divided by cos x- 2x = x^n+1

what do i do from there

thanks so much!!!!

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- Dec 8th 2009, 06:44 PMcalculusisnotfunnewton's method
having a little trouble with newton's method.

sin x = x^2; x>0

i found the equation after newtons to be:

x-sin x-x^2 divided by cos x- 2x = x^n+1

what do i do from there

thanks so much!!!! - Dec 8th 2009, 08:12 PMTKHunny
Wow. First and foremost, please go review some early concepts such as Order of Operations. Then, you may wish to contemplate the use of SUBscripts. Third, just a little LaTeX would go a very long way. Fourth, why write things in confusing orders when perfectly clear orders are avilable? Finally, write a clear definition of the task: For $\displaystyle f(x) = x^{2} - \sin(x)$ Solve f(x) = 0 for x.

$\displaystyle x_{n+1} = x_{n} - \frac{x_{n}^{2}-\sin(x_{n})}{2x_{n} - \cos(x_{n})}$

Now, pick a starting point. You may wish to stay away from x = 0, as that is a trivial solution. (Very wisely, your problem statement excludes x = 0, so this should not be a problem.) A quick glance at the graph shows that x = 1 might be a good place to start.

$\displaystyle x_{0} = 1$

$\displaystyle x_{1} = 0.891396$

$\displaystyle x_{2} = 0.876985$

$\displaystyle x_{3} = 0.876726$

Plug-n-chug.

Calculus is a delight if you shore up your process and quit stabbing in the dark. (Wink)