How do you solve e^(-x)-x+2=0?

1 Answer
Jun 21, 2016

2.1200, nearly.

Explanation:

If LHS is f(x), f(2)=0.135... > 0 and f(3)=-0.950...<0.

So, the root in (2, 3)

Use the method of successive approximation, from the difference

equation

x_n=2+e^(-(x_(n-1))), n = 1, 2, 3, ..,

with the starter guess-value x_0=2,

we obtain the sequence of approximations

2.21..., 2.118..., 2.1202.., 2.1200.., 2.1200..

f(2.12)=O(10^(-5)).

f(x) is a decreasing function and, therefore, the root is unique.

Important note:
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. .