eframath – Página Personal

Here is example of a page with LaTeX formulas (how it appears in WordPress editor):

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

(1) $\begin{equation*} P_{N-1}(x)=\sum_{j=0}^{N-1}{a_jx^j} \end{equation*}$

Its coefficients $\{a_j\}$ are found as a solution of system of linear equations:

(2) $\begin{equation*} \left\{ P_{N-1}(x_k) = f_k\right\},\quad k=-\frac{N-1}{2},\dots,\frac{N-1}{2} \end{equation*}$

Here are references to existing equations: (1), (2).
Here is reference to non-existing equation (??).

Same page processed by QuickLaTeX and published (how visitors see it in a browser):

QuickLaTeX Example

For the display environments, equation numbering is automatic, but this may be overridden and the number set explicitly with \tag{..} placed within the display expression.

A number of options may be set for an expression with attribute tags such as size, color, background, align, as arguments of \quicklatex{} placed within the expression:

$\boxed{f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1}$

renders with green font of 25 pixels height:

QuickLaTeX Example

Compilation of an expression may be suppressed, showing instead the LaTeX source, by preceding the expression with a !.

For mathematical graphs you may use tikzpicture and pgfplots, e.g. :

Rendered by QuickLaTeX.com

compiles to

QuickLaTeX Example

see on-line tikz help for examples and more information.

Whether or not QuickLaTeX has been activated with , you may always place a LaTeX expression within $..$ shortcodes everywhere on the site. Attribute tags are allowed: $...$ .

Visit QuickLaTeX’s home page for more information on features, examples, tips & tricks, tikZ graphics inclusion, etc.

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Olimpiada Matemática