Using Newton's Method to Solve Transcendental Equations
Newton's method is most useful when applied to complicated
functions where we have no way to get an algebraic solution, even
with the help of a computer. For instance, solving ex+x=4
is the same as finding the roots of f(x)=ex+x−4. As always,
we have xn+1=xn−f(xn)f′(xn),