i have $\tan^{-1}(x)-\sin(x)+\frac{1}{3}=0$ and i need to find range of $x$ that converge with newton method please help me how do i do this
#please help me
verbal seal
buoyant oarBOT
goat
crystal treeBOT
i have $\tan^{-1}(x)-\sin(x)+\frac{1}{3}=0$ and i need to find range of $x$ that...
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verbal seal
@urban helm @zealous depot
zealous depot
yo
verbal seal
where to start
verbal seal
take derivative and set up newton method is $f(x)=\tan^{-1}(x)-\sin(x)+\frac{1}{3}$ and $f'(x)=\frac{1}{1+x^{2}}-\cos(x)$
buoyant oarBOT
goat
zealous depot
$x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$
buoyant oarBOT
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buoyant oarBOT
curry supplier
verbal seal
yes i know so here $x_{n+1}=x_{n}-\frac{\tan^{-1}(x_{n})-\sin(x_{n})+\frac{1}{3}}{\frac{1}{1+x_{n}^{2}}-\cos(x_{n})}$ but where converge
buoyant oarBOT
goat
verbal seal
lets say our initial guess $(x_0) = 0$
i know how to do this but what is the where it converges vs diverges
find where converges and prove converge there
zealous depot
idk
i think you should guess some values between 0-1 (i think 1/2 is a good start) and then estimate the roots
verbal seal
lets say our initial guess $(x_0) = 0$
btw run thru this it doesnt converge
verbal seal
same question for halleys method $x_{n+1}=x_{n}-\frac{2f(x_{n})f'(x_{n})}{2(f'(x_{n}))^{2}-f(x_{n})f''(x_{n})}$
buoyant oarBOT
goat
verbal seal
@cunning olive
cunning olive
Say you have an interval I containing the solution
f’(x) shouldn’t be 0 for all values of x in I
And k should be less than 1, where k is $\max_{x \in [a,b]} \left\lvert \frac{f''(x)}{2,f'(x)} \right\rvert.$
buoyant oarBOT
a_g3nt
cunning olive
So basically just pick an interval, make sure that for any x in the interval, f’(x) isn’t 0
You can do this by making sure at both extremes, it’s either both positive or both negative.
Compute k and make sure k<1
All values in this interval should work
@verbal seal
This is the best I can come up with
indigo yokeBOT
@verbal seal
indigo yokeBOT
@cunning olive @zealous depot The user still needs help with this help request.
cunning olive
@verbal seal. you there?