Use Newton's method to approximate a root of the equation 4sin(x)=x\displaystyle {4}{\sin{{\left({x}\right)}}}={x} as follows.
Let x1=1\displaystyle {x}_{{1}}={1} be the initial approximation.
The second approximation x2\displaystyle {x}_{{2}} is  
and the third approximation x3\displaystyle {x}_{{3}}is