I am given the function $x(t)=4\mathrm{arctan}t$ and told that routine computations will show that $x(0)=0$ and $x(1)=\pi $.

I must determine a differential equation for $x(t)$ of the form ${x}^{\prime}(t)=f(t,x)$.

I must then use $f$ to approximate $\pi $.

I will use Euler's Method to find minimum number of iterations ($n$) needed to yield the approximation $\pi \approx 3.1400$, such that $n-1$ iterations is strictly less than 3.1400.

How do I find $n$? It seems to me that it can't be found given the instruction set that I am provided.

I must determine a differential equation for $x(t)$ of the form ${x}^{\prime}(t)=f(t,x)$.

I must then use $f$ to approximate $\pi $.

I will use Euler's Method to find minimum number of iterations ($n$) needed to yield the approximation $\pi \approx 3.1400$, such that $n-1$ iterations is strictly less than 3.1400.

How do I find $n$? It seems to me that it can't be found given the instruction set that I am provided.