This page uses many of the same examples seen in the documentation page. Most examples are given both in-line and displayed style, but some were too large for reasonable in-line presentation. The last example shows a more extensive presentation involving several expressions.
Example 1:
CPT source: \int[v:x][l:0][u:\pi;]{\sin{x}}=2
Inline:
Displayed:
Example 2:
CPT source: \limit[v:x][c:{x\tendsto@above|0}]{\sin{x}/x}=1
Inline:
Displayed:
Example 3:
CPT source:
=0
\end{piece}
\begin{otherwise}
-x
\end{otherwise}
\end{piecewise}]]>
Displayed:
Example 4:
CPT source: x_1=(-b+\root{b^2-4a*c})/2a
Inline:
Displayed:
Example 5:
CPT source: \sum[v:n][l:1][u:\infinity;]{1/n^2}=\pi;^2/6
Inline:
Displayed:
Example 6:
CPT source:
\begin{matrix}
\begin{matrixrow}
\cos{θ} (-\sin{θ})
\end{matrixrow}
\begin{matrixrow}
\sin{θ} \cos{θ}
\end{matrixrow}
\end{matrix}
Displayed:
Example 7:
CPT source:
\int[v:x][l:-\infinity;][u:\infinity;]
{\exp{-(x^2)}}=\root{\pi;}
Inline:
Displayed:
Example 8:
CPT source:
\diff[v:x]{
\int[v:t][l:a][u:x]{f(t)}
}=f(x)
Inline:
Displayed:
Example 9:
CPT source:
\begin{apply}
\partialdiff[s:x y]{f} x y
\end{apply}
=\partialdiff[v:x][v:y]{f(x,y)}
Inline:
Displayed:
Example 10: Stokes' Theorem (for surface integrals in space)
CPT source:
Displayed:
Example 11: Taylor Polynomials (displayed)
The first three Taylor polynomial approximations to
f(x), centered at c, are:
In general:
where the kth Taylor remainder, R_k(x), is given by:
for some value of between x and c, provided \diff[n:k+1]{f} is continuous between x and c (which implies that all lower derivatives, including f itself, are also continuous on that interval).