# Newton's Method

#### toasted

1. Homework Statement

Find, to three decimal places, the value of x such that e-x = x. Use Newton's method.

2. Homework Equations

3. The Attempt at a Solution
I looked up what Newton's method was and I found that it was

f(x)= $$\int x$$ = f(xo) + f](xo)(x-xo)

But I dont understand how I can apply it to this problem. Could someone just help me set up the problem, and I should be able to figure the problem from there. Thanks!

Last edited by a moderator:
Related Calculus and Beyond Homework Help News on Phys.org

#### Dick

Science Advisor
Homework Helper
You are trying to solve f(x)=e^x-x=0. Newton's method tells you how to turn an initial guess for a solution x0 into a better approximation of a solution, x1. x1=x0-f'(x0)/f(x0). Take an initial guess at the solution and try it out.

#### HallsofIvy

Science Advisor
Homework Helper
1. Homework Statement

Find, to three decimal places, the value of x such that e-x = x. Use Newton's method.

2. Homework Equations

3. The Attempt at a Solution
I looked up what Newton's method was and I found that it was

f(x)= $$\int x$$ = f(xo) + f](xo)(x-xo)

But I dont understand how I can apply it to this problem. Could someone just help me set up the problem, and I should be able to figure the problem from there. Thanks!
That is certainly NOT "Newton's method" for solving equations. The left side looks like the formula for the tangent line at $x_0$ and it is certainly not equal to f(x) (I don't know how the integral got in there).

As Dick said, to solve f(x)= 0, choose some starting value $x_0$ and iterate:
[tex]x_{n+1}= x_n- \frac{f(x_n)}{f'(x_n)}[/itex]
until you have sufficient accuracy.

Here, $f(x)= e^{-x}- x$ and either $x_0= 0$ or $x_0= 1$ will do.

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving