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

##### 1 Answer

Jun 21, 2016

2.1200, nearly.

#### Explanation:

If LHS is

So, the root in (2, 3)

Use the method of successive approximation, from the difference

equation

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.

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. .