A charged particle having drift velocity of \(7.5 \times10^{-4}ms^{-1}\) in an electric field of \(3\times10^{-10}Vm^{-1}\) has a mobility (in \(m^2V^{-1}s^{-1}\)) of

At first, we sample \(f(x)\) in the \(N\) ( \(N\)  is odd) equidistant points around \(x^*\):

\[
   f_k = f(x_k),\: x_k = x^*+kh,\: k=-\frac{N-1}{2},\dots,\frac{N-1}{2}
\]
where  \(h\)  is some step.
Then we interpolate points \(\{(x_k,f_k)\}\) by polynomial
\begin{equation} \label{eq:poly}
   P_{N-1}(x)=\sum_{j=0}^{N-1}{a_jx^j}
\end{equation}
Its coefficients \(\{a_j\}\) are found as a solution of system of linear equations:
\begin{equation} \label{eq:sys}
   \left\{ P_{N-1}(x_k) = f_k\right\},\quad k=-\frac{N-1}{2},\dots,\frac{N-1}{2}
\end{equation}
Here are references to existing equations: (\ref{eq:poly}), (\ref{eq:sys}).
Here is reference to non-existing equation (\ref{eq:unknown}).

\(\ce{2H2 + O2 -> 2H2O}\)

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