### 4.3.1 Approximate solution of an equation : `newton`

`newton` takes as arguments : an expression `ex`, the variable name of this expression (by default `x`), and three values `a` (by default `a=0`), `eps` (by default `eps=1e-8`) and `nbiter` (by default `nbiter=12`).
`newton(ex,x,a,eps,nbiter)` computes an approximate solution `x` of the equation `ex=0` using the Newton algorithm with starting point `x=a`. The maximum number of iterations is `nbiter` and the precision is `eps`.
Input :

`newton(x```^```2-2,x,1)`

Output :

`1.41421356237`

Input :

`newton(x```^```2-2,x,-1)`

Output :

`-1.41421356237`

Input :

`newton(cos(x)-x,x,0)`

Output :

`0.739085133215`