kth.cs.math.base-course{sf1671}.seminar.1.homework.template.tex

sf1671-sem1-hw-template.tex

% !TEX options = -shell-escape -interaction=batchmode "%DOC%"
% brew install gnuplot; gnuplot *.gnuplot # after each plot formula change
\documentclass[a4paper,10pt]{article}
\usepackage{amsmath}
\usepackage[margin=2cm]{geometry}
\usepackage[shortlabels]{enumitem}
\usepackage{bbm}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\usepackage{wrapfig}
\usepackage{graphicx}
\usepackage{sidecap}
\usepackage{caption}

\renewcommand{\thesubsubsection}{\thesubsection. \alph{subsubsection})}

\title{Seminarium 1 - SF1671}
\author{Leonard Pauli}
\date{2 sep 2020}

\begin{document}

\maketitle

\section{}
\subsection{Lös ekvationen $|x-2|\cdot|x+2|+|2x+1|=3$}

	\begin{SCfigure}[][h]
		\begin{minipage}{0.4\textwidth}
			$$x = \begin{cases}
				x &\text{if } x \ge 0\\
				-x &\text{if } x < 0
			\end{cases}$$
		\end{minipage}

		\begin{minipage}{0.5\textwidth}
			\begin{tikzpicture}[domain=-3:3]
				\draw[very thin,color=gray] (-3,0) grid (3,3);
				\draw[->] (-3,0) -- (3,0) node[right] {$x$};
				\draw[->] (0,0) -- (0,3) node[above] {$y$};
				\draw[color=red] plot[id=x2] function{abs(x)} node[right] {$y=|x|$};
			\end{tikzpicture}
		\end{minipage}
		\captionsetup{labelformat=empty}
	\end{SCfigure}

	\begin{align}
		4^x * 2^{x^2} &= 8^{x^3}\\
		4^x * 2^{x^2} &= 8^{x^3}\tag{some note}\\
		x &= 72
	\end{align}

	\dots

\clearpage
\subsection{}
\subsubsection{Lös ekvationen $\frac{5}{x-2}=\frac{6}{x-1}+\frac{14}{x+1}+\frac{9}{x+2}$}

	\dots

\subsubsection{Bestäm för vilka $x\in\mathbbm{R}$, $\frac{5}{x-2}\ge\frac{6}{x-1}+\frac{14}{x+1}+\frac{9}{x+2}$}

	\dots

\clearpage
\subsection{Finn alla lösningar till ekvationen $$\log_3(56+4^{x+1}) = \log_3(2+3\cdot2^x) + \log_3(7+2^x)$$}

	\dots

\clearpage
\subsection{Lös ekvationen $\arctan(\cot x) = -\tfrac{\pi}{3}$}

	\dots


\end{document}

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