use newtons method to find the roots of the equation
sinx=x^(2)+3^(x)-1
correct to sic decimal places
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
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!