This is an example of a theory module in Ximera, with some useful environments and commands.
It is advisable to also view the PDF version, where this remark suggests to consult
the Online version.
Use \begin{definition} for definitions, and \begin{exercise} for exercises.
The absolute value of a real number , denoted by , is \[ |a| \perdef \begin{cases} \phantom{-}a & \text{if } a \geq 0 \\ -a & \text{if } a<0. \end{cases} \]
Familiarize yourself with the (interactive!) graph of the cosine function:
(via Desmos, implemented as \graph[xmin=-5,xmax=20,ymin=-1,ymax=1]{y=cos(x)})
\[ \graph [xmin=-5,xmax=20,ymin=-1,ymax=1]{y=cos(x)} \]
Remarks can simply be included in the running text, or by using \begin{remark}:
Properties of the absolute value (with )
- (a)
- Be careful: , but definitely not
is incorrect if . Indeed, if , then
- (b)
- , because is always positive.
Examples use \begin{example}. By default, examples also provide the correct answer in the handout version, while that is not the case for the exercises.
2024-07-15 10:40:52