Newton's Method

To solve

(1)
\begin{equation} {e}^{x}-x=2 \end{equation}

Write a function

(2)
\begin{equation} f(x)={e}^{x}-x-2 \end{equation}

Guess ${x}_{1}$, any constant you like

(3)
\begin{align} {x}_{2}={x}_{1}-\frac{f({x}_{1})}{f'({x}_{1})} \end{align}
(4)
\begin{align} {x}_{3}={x}_{2}-\frac{f({x}_{2})}{f'({x}_{2})} \end{align}

The solution x will get closer and closer to the really value.

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