[quicklatex]
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: (eq:poly), (eq:sys).
Here is reference to non-existing equation (eq:unknown).
\[
\quicklatex{color="#00ff00" size=25}
\boxed{f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1}
\]
\begin{tikzpicture}
[+preamble]
\pgfplotsset{compat=newest}
[/preamble]
\begin{axis}
\addplot3[surf,domain=0:360,samples=40] {cos(x)*cos(y)};
\end{axis}
\end{tikzpicture}
\begin{tikzcd}
& P \arrow[d, "f"'] \arrow[dl, "g", dashed] \\
M \arrow[r, "p"'] & N \arrow[r] & 0
\end{tikzcd}
\begin{tikzpicture}
\draw (0,0) circle [radius=2cm];
\draw (0,0) -- (2,0);
\filldraw [black] (0,0) circle (2pt) node[anchor=north] {O};
\filldraw [black] (2,0) circle (2pt) node[anchor=north] {A};
\node at (1, 0.2) {r};
\end{tikzpicture}
[/quicklatex]