More analysis

[cinder abyss]

So I tried using Taylor’s Theorem on $f(x)$ and got some absolutely monstrous expression…

Then I tried it on $$g(x)=x-\frac{f(x)}{f’(x)}$$ and got to $$x_{n+1}-\xi = \frac{f(t_n)f’’(t_n)}{(f’(t_n))^2}(x_n-\xi)$$ and now I’m stuck. Any ideas?

[jolly needle]

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[proud zinc]

ℝανι-sαη
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[cinder abyss]

Part c is what I need help with

[cinder abyss]

Part a I’ve watched enough videos
Part b, I showed that x_n is monotonic decreasing and bounded, then showed that the limit had to be the fixed point
Part c I’m dying

[runic vine]

geometry.

[cinder abyss]

That doesn’t help

How is geometry supposed to help

Βιτch still has me blocked

How the hell do I use geometry here

So I take some random ass monotonic once-differentiable function and then what??

@runic vine elaborate

[cinder abyss]

Nvm done

Had to expand f(ξ) at x_n

+close

[silk scarab]

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