Testing MathJax-LaTeX

https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference

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} \tag{1}
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} \tag{asdf}
\left\{ P_{N-1}(x_k) = f_k\right\},\quad k=-\frac{N-1}{2},\dots,\frac{N-1}{2}
\end{equation}
\begin{equation} \label{eq:sys2} \tag{asdf2}
\{ P_{N-1}(x_k) = f_k\},\quad k=-\frac{N-1}{2},\dots,\frac{N-1}{2}
\end{equation}

Backslash left and right parentheses:

\[ \left( \frac{1}{2} \right) \qquad ( \frac{1}{2} ) \\ ( \frac{1}{2} ) \]
\[ \left( \frac{1}{2} \right) \qquad \left( \frac{1}{2} ) \]

$$ 1 \quad \frac ab \quad 2 \quad \frac{c}{d} \quad 3 \quad {e \over f} \quad 4 \quad {}^g/_h \quad 5 \quad i/j \quad 6 \quad $$

$$ 1+1=2 \textrm{ centered equation } 1+1=2 $$

\( 1+1=2 \textrm{ left equation } 1+1=2 \)

\begin{align}
1 + 1 & = 2.00000000 \textrm{ aligned to character}\\
& = 2.0000000000000000 \\
& = 1.99999999999 \\
\end{align}

Here are references to existing equations: \ref{eq:poly}, \eqref{eq:sys}.
Here is reference to non-existing equation \eqref{eq:unknown}.

 

\begin{equation}
X=
\begin{cases}
0, & \text{if}\ a=1 \\
1, & \text{otherwise}
\end{cases}
\end{equation}

$$ \lim_{x\to 1} $$

\( \lim_{x\to 1} \)

 
 

$$ default, \it Italics, \bf bold,   \sf sans serif,   \tt typewriter, \rm default Roman, \it italics $$

$$horizontal spacing: back slash\ comma\, ! \! > \> : \: ; \; enspace \enspace quad \quad qquad \qquad end$$

$$hskip1point \hskip1pt hskip2point \hskip 2pt hskip10point \hskip10pt hskip3point \hskip 3pt 1ex \hspace{1ex} 1em \hspace{1em} 2em \hskip2em lengthofasdf \hphantom{<asdf>} backslash \ tilde ~ end$$

$$\tiny tiny$$

$$default$$

$$\scriptsize scriptsize \small small \normalsize normalsize or default, \large large$$

$$\normalsize normalsize or default, \large large$$

$$\Large Large \LARGE LARGE \huge huge \Huge Huge1$$

$$\Large  \LARGE  \huge  \Huge Huge2$$

$$\Huge Huge3$$

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