Thread: newton'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!!!!

Originally Posted by calculusisnotfun

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!!!!

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.