use newtons method to find the roots of the equation

sinx=x^(2)+3^(x)-1

correct to sic decimal places

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- Dec 7th 2008, 01:11 PMthecountnewton's method
use newtons method to find the roots of the equation

sinx=x^(2)+3^(x)-1

correct to sic decimal places - Dec 7th 2008, 08:36 PMCaptainBlack
Newton's methof gives us an itterative methof for finding a root of the equation $\displaystyle f(x)=0$. This is:

$\displaystyle x_{n+1}=x_n-\frac{f(x)}{f'(x)}$

So for this we have:

$\displaystyle f(x)=x^2+3^x-1-\sin(x)$

with:

$\displaystyle f'(x)=2x+\ln(3)3^x-\cos(x)$

Now you need an initial guess, well there is an obvious root at $\displaystyle x=0$, and a bit of investigation suggests that there is another root to the left of this, so we could take an initial guess $\displaystyle x=-1$.

CB - Dec 8th 2008, 12:05 AMJameson
You should understand the theory behind this method, but here is a cool online tool to help check if you're doing it correctly.

Newton's Method

Don't cheat though!