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Finding approximate solutions to equations f(x)=0f(x) = 0f(x)=0.
xn+1=xn−f(xn)f′(xn)x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}xn+1=xn−f′(xn)f(xn)
f(x)f(x)f(x) is the function; f′(x)f'(x)f′(x) is its derivative.
An initial guess x0x_0x0 for the root.
Ensure ∣xn+1−xn∣<ε|x_{n+1} - x_n| < \varepsilon∣xn+1−xn∣<ε for desired tolerance.
Choose an initial approximation for the solution.
The method may fail or converge slowly.
It may converge to the wrong root or fail to converge.
The method may converge to different roots based on x0x_0x0.
Graphically or analytically assess the function.
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