# Informatics1-2017/HW5

Reproduce the following pdf document using latex: homework5.pdf

In the email attach the .tex and the .pdf files only.

### Help

These are the commands that we didn't use on the practical or the lecture, but are still required to create some of the formulas in the homework:

\lim        % limit, example: \lim_{x\to \infty}
\in         % element symbol
\notin      % element symbol striked through
\cos        % cosinus
\sin        % sinus
\cdot       % center dot (to emphasize multiplication
\qquad      % big space in math mode
\mapsto     % "maps to" arrow
\backslash  % backwards slash: \
\ln         % logarithm
\prod       % product
\sqrt[k]{n} % kth root of n
\min        % minimum
\max        % maximum

For most sections I used the align* environment to write stuff in multiple lines, using the following format:

\begin{align*}
&formula1 &&formula2 &&formula3, \\
&formula4 &&formula5 &&formula6
\end{align*}

The first & aligns the formulas, and every second & creates some whitespace between the formulas.

I used the following format for the cases enviroment:

function \qquad x \mapsto \begin{cases}
value1, &\text{ if } condition1 \text{ and } condition2 \\
value2, &\text{ if } condition2
\end{cases}

A little help with the title: you can put a \\ (newline) command in the title as well.