How do you solve # e^(-x)-x+2=0#?
If LHS is
So, the root in (2, 3)
Use the method of successive approximation, from the difference
with the starter guess-value
we obtain the sequence of approximations
2.21..., 2.118..., 2.1202.., 2.1200.., 2.1200..
f(x) is a decreasing function and, therefore, the root is unique.
Despite that we get a good approximation to the solution of the given equation, this sequence converges to the solution of the difference equation and not the solution of the given equation, in mathematical exactitude. .