# Use Euler's method with step size 10^-n to estimate x(1), where f(x) is the solution of the initial-value problem below. f(x)=-x x(0)=1

Use Euler's method with step size $10^{-n}$ for $n=1,2,3,4.$ to estimate $x(1)$, where $f(x)$ is the solution of the initial-value problem below.

$x'=f(x)=-x$

$x(0)=1$

EDIT / UPDATE:

x_n+1=x_n + f(x_n)h

how does it become x_n+1= x_n[(1-h)^(n+1)]

Solution then is X(1)=X_n where n=[1/h]

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Why not simply edit your previous question? – Arkamis Oct 31 '12 at 19:32
thanks, Khanak; reposting/editing keeps the problem/work altogether, in one location, and when you edit/answer a problem, it gets kicked up to the front of the "active" posts, so it won't get lost or overlooked. I'll add "EDIT" to your post, so those who have read the post previously see your update more readily.... – amWhy Oct 31 '12 at 22:09

\begin{align*} x_0 &= x(0), \\ x_n &= x_{n-1}+hf(x_{n-1}). \end{align*}
For $h = 10^{-n}$, $x_{10^n} = x(1)$.