# Using the Euler Method with the step size triangle t=1, estimate x(1) numerically.

$f\left(x\right)=-x$ and initial condition $x\left(0\right)=1$
Using the Euler Method with the step size $\mathrm{\Delta }t=1$, estimate $x\left(1\right)$ numerically.
I so far did:
${X}_{n+1}={X}_{n}+f\left({x}_{n}\right)\left(1\right)$
${X}_{1}=0$
${X}_{2}=0$
I have a similar question on my test tomorrow. Any help will be appreciated
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Baron Coffey
Presumably the differential equation you are working with is ${x}^{\prime }=-x$ with initial condition $x\left(0\right)=1$ and the capital $X$'s are the calculated points. You have done the iteration correctly, getting $x\left(1\right)=0$. Analytically we can see that the solution is $x={e}^{-t}$, so the correct $x\left(1\right)=\frac{1}{e}$. You could blacko it with a smaller step size and see that it is more accurate, but that isn't asked for in the question.
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Kwenze0l
For you +1 for simply interpreting the question