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diff --git a/mat/domace_naloge/32/dokument.tex b/mat/domace_naloge/32/dokument.tex new file mode 100644 index 0000000..e0516c4 --- /dev/null +++ b/mat/domace_naloge/32/dokument.tex @@ -0,0 +1,230 @@ +% !TeX encoding = UTF-8 +% !TeX spellcheck = sl_SI +% do-vimlatex-onwrite +\documentclass[]{article} +\usepackage[utf8]{inputenc} +\usepackage{etoolbox} +\usepackage[hidelinks]{hyperref} +\usepackage{xurl} % da breaka url +\usepackage[a4paper, total={7in, 10in}]{geometry} +\usepackage{graphicx} +\usepackage{hologo} +\usepackage{amssymb} +\usepackage{calculator} +\usepackage{pgfplots} +\usepackage[inline]{enumitem} +\usepackage{siunitx} +\usepackage{multicol} +\usepackage{tabularcalc} +\usepackage{amsmath} +\usepackage{float} +\usepackage{tasks} +\usepackage{filecontents} +\usepackage{textcomp} +\usepackage{tkz-euclide} +\usepackage{dirtytalk} +\usepackage{csquotes} +\usepackage{listings} +\usepackage{datetime} % [ddMMyyyy] +\usepackage{ccicons} +\usepackage{chemformula} +\usepackage{gensymb} +\usepackage[normalem]{ulem} +\usepackage[slovene]{babel} +\usepackage{cancel} +\usepackage{tabularx} +\usepackage{xcolor} +\usepackage{colortbl} +\usepackage{exsheets} +\usepackage{harpoon} +\usepackage{readarray} +\usepackage{forloop} +\usepackage[nomessages]{fp} +\usepackage{multirow} +\newcolumntype{Y}{>{\centering\arraybackslash}X} +% \usepackage{multienum} % weird with labels +\usetikzlibrary{calc} %% not really needed............. idk. +%\usetikzlibrary{external} +% \usetkzobj{all} % tkz-euclide > 3.02 tega ne potrebuje več (: +%\tikzexternalize +\sisetup{output-decimal-marker = {,}, quotient-mode=fraction,per-mode=fraction} % per-mode=symbol +\newcommand\ddfrac[2]{\frac{\displaystyle #1}{\displaystyle #2}} +\newcommand{\functionSamples}{1000} % fix to fancier value upon release, keep low during development +\newcommand{\razhroscevanje}{1} +\definecolor{codegreen}{rgb}{0,0.6,0} +\definecolor{codered}{rgb}{1,0,0} +\definecolor{codegray}{rgb}{0.5,0.5,0.5} +\definecolor{codepurple}{rgb}{0.58,0,0.82} +\definecolor{backcolour}{rgb}{0.95,0.95,0.92} +\renewcommand{\dateseparator}{. } +\settimeformat{hhmmsstime} +\lstdefinestyle{mystyle}{ + backgroundcolor=\color{backcolour}, + commentstyle=\color{codegreen}, + keywordstyle=\color{magenta}, + numberstyle=\tiny\color{codegray}, + stringstyle=\color{codepurple}, + basicstyle=\ttfamily\footnotesize, + breakatwhitespace=false, + breaklines=true, + captionpos=b, + keepspaces=true, + numbers=left, + numbersep=5pt, + showspaces=false, + showstringspaces=false, + showtabs=false, + tabsize=2 +} +\lstset{style=mystyle} +\def\@maketitle{% + \newpage + \null + \vskip 2em% + \begin{center}% + \let \footnote \thanks + {\LARGE \@title \par}% + \vskip 1.5em% + {\large + \lineskip .5em% + \begin{tabular}[t]{c}% <------ + \@author% <------ Authors + \end{tabular}\par}% <------ + \vskip 1em% + {\large \@date}% + \end{center}% + \par + \vskip 1.5em} +%opening +\newcommand{\snovdn}{Potenčna funkcija z naravnim eksponentom } +\newcommand{\predmdn}{mat} +\newcommand{\predmkaj}{domace\_naloge} +\newcommand{\stevilkadn}{32} +\newcommand{\cm}[1]{\SI{#1}{\centi\meter}} +\newcommand{\kmh}[1]{\SI{#1}{\kilo\meter\per\hour}} +\makeatletter +\newcommand{\xslalph}[1]{\expandafter\@xslalph\csname c@#1\endcsname} +\newcommand{\@xslalph}[1]{% + \ifcase#1\or a\or b\or c\or \v{c}\or d\or e\or f\or g\or h\or i% + \or j\or k\or l\or m\or n\or o\or p\or r\or s\or \v{s}% + \or t\or u\or v\or z\or \v{z} + \else\@ctrerr\fi% +} +\AddEnumerateCounter{\xslalph}{\@xslalph}{m} +\makeatother +\newcommand\gauss[2]{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))} % Gauss function, parameters mu and sigma +\newcommand*\textfrac[2]{ + \frac{\text{#1}}{\text{#2}} +} +\NewTasks[counter-format=\xslalph*),label-format=\bfseries]{primerTasks}(3) +\newcommand\vektor{\overrightarrow} +\newcommand{\iic}{I\textsuperscript{2}C } +\title{% + \snovdn --- \stevilkadn. domača naloga + \\ + \large Matematika, Gimnazija Bežigrad} +\author{\begin{tabular}{rl} + \textbf{Profesor:} & prof. Vilko Domajnko \\ + \textbf{Avtor:} & Anton Luka Šijanec, 2. a +% \textbf{Avtor:} & Anton Luka Šijanec \\ & Member 2 \\ & Member 3 +\end{tabular}} +\newcommand\hcancel[2][black]{\setbox0=\hbox{$0#2$}% +\rlap{\raisebox{.45\ht0}{\textcolor{#1}{\rule{\wd0}{1pt}}}}#2} +\everymath{\displaystyle} % https://tex.stackexchange.com/a/32847/212260 +\begin{document} +\maketitle +\begin{abstract} +Ta dokument vsebuje navodila in rešitve domače naloge snovi \textit{\snovdn}pri matematiki, ki sem jih spisal sam. +\end{abstract} +\paragraph{Navodilo naloge} \textbf{vaje2} 117 / 754 -- 760 (2 sodi, 2 lihi) +%\tableofcontents +\begin{enumerate}[label=\textbf{\arabic*.}] % 758, 754, 759, 755 + \setcounter{enumi}{753} + \item Nariši grafe funkcij. + \begin{multicols}{4} + \begin{enumerate}[label=\textbf{\xslalph*)}] + \item $f(x)=x^3$ + \item $g(x)=(x-1)^3$ + \item $h(x)=x^3-1$ + \item $m(x)=\frac{1}{2}x^3$ + \end{enumerate} + \end{multicols} + \begin{tikzpicture} + \begin{axis}[grid = both, grid style={line width=.1pt, draw=gray!10}, minor tick num = 1, xstep = 1, ystep = 1, xtick={-6,...,6}, ytick={-6,...,6}, ymin=-6, domain=-6:6, major grid style={line width=.2pt,draw=gray!50},scale only axis, x = 10mm, y = 10mm, ymax=6, samples=\functionSamples, axis lines = middle, xlabel = $x$, ylabel = {$y$}, xmin=-6, xmax=6, legend style={at={(1,1)},anchor=north west}] + \addplot[black, solid] (x, {x^3}); + \addlegendentry{$f(x)=x^3$} + \addplot[black, densely dashed] (x, {(x-1)^3}); + \addlegendentry{$g(x)=(x-1)^3$} + \addplot[black, densely dotted] (x, {x^3-1}); + \addlegendentry{$h(x)=x^3-1$} + \addplot[black, densely dashdotdotted] (x, {(-1/2)*x^3)}); + \addlegendentry{\raisebox{7pt}{$m(x) = -\frac{1}{2}x^3$}} + \end{axis} + \end{tikzpicture} + \newpage + \item Nariši grafe funkcij. + \begin{multicols}{4} + \begin{enumerate}[label=\textbf{\xslalph*)}] + \item $f(x)=-x^2$ + \item $g(x)=2-x^2$ + \item $h(x)=(x+1)^2+2$ + \item $m(x)=|x^2-1|$ + \end{enumerate} + \end{multicols} + \begin{tikzpicture} + \begin{axis}[grid = both, grid style={line width=.1pt, draw=gray!10}, minor tick num = 1, xstep = 1, ystep = 1, xtick={-6,...,6}, ytick={-6,...,6}, ymin=-6, domain=-6:6, major grid style={line width=.2pt,draw=gray!50},scale only axis, x = 10mm, y = 10mm, ymax=6, samples=\functionSamples, axis lines = middle, xlabel = $x$, ylabel = {$y$}, xmin=-6, xmax=6, legend style={at={(1,1)},anchor=north west}] + \addplot[black, solid] (x, {-x^2}); + \addlegendentry{$f(x)=-x^2$} + \addplot[black, densely dashed] (x, {2-x^2}); + \addlegendentry{$g(x)=2-x^2$} + \addplot[black, densely dotted] (x, {(x+1)^2+2}); + \addlegendentry{$h(x)=(x+1)^2+2$} + \addplot[black, densely dashdotdotted] (x, {abs(x^2-1)}); + \addlegendentry{$m(x)=|x^2-1|$} + \end{axis} + \end{tikzpicture} + \setcounter{enumi}{757} + \newpage + \item Nariši graf funkcije $f(x)=\frac{1}{2}(x+2)^3-1$. + + \begin{tikzpicture} + \begin{axis}[grid = both, grid style={line width=.1pt, draw=gray!10}, minor tick num = 1, xstep = 1, ystep = 1, xtick={-6,...,6}, ytick={-6,...,6}, ymin=-6, domain=-6:6, major grid style={line width=.2pt,draw=gray!50},scale only axis, x = 10mm, y = 10mm, ymax=6, samples=\functionSamples, axis lines = middle, xlabel = $x$, ylabel = {$y$}, xmin=-6, xmax=6, legend style={at={(1,1)},anchor=north west}] + \addplot[black, solid] (x, {(1/2)*(x+2)^3-1}); + \addlegendentry{\raisebox{7pt}{$f(x)=\frac{1}{2}(x+2)^3-1$}} + \end{axis} + \end{tikzpicture} + \newpage + \item Nariši grafe funkcij $f(x)=1-(x-1)^2$, $g(x)=|f(x)|$, $h(x)=f(|x|)$ in $k(x)=|f(|x|)|$. + + \begin{tikzpicture} + \begin{axis}[grid = both, grid style={line width=.1pt, draw=gray!10}, minor tick num = 1, xstep = 1, ystep = 1, xtick={-6,...,6}, ytick={-6,...,6}, ymin=-6, domain=-6:6, major grid style={line width=.2pt,draw=gray!50},scale only axis, x = 10mm, y = 10mm, ymax=6, samples=\functionSamples, axis lines = middle, xlabel = $x$, ylabel = {$y$}, xmin=-6, xmax=6, legend style={at={(1,1)},anchor=north west}] + \addplot[black, solid] (x, {1-(x-1)^2}); + \addlegendentry{$f(x)=1-(x-1)^2$} + \addplot[blue, densely dashed] (x, {abs(1-(x-1)^2)}); + \addlegendentry{$g(x)=|f(x)|$} + \addplot[green, densely dashed] (x, {1-(abs(x)-1)^2}); + \addlegendentry{$h(x)=f(|x|)$} + \addplot[red, densely dashdotdotted] (x, {abs(1-(abs(x)-1)^2)}); + \addlegendentry{$k(x)=|f(|x|)|$} + \end{axis} + \end{tikzpicture} +\end{enumerate} +\section{Zaključek} +Ta dokument je informativne narave in se lahko še spreminja. Najnovejša različica, torej PDFji in +\hologo{LaTeX}\footnote{Za izdelavo dokumenta potrebujete \texttt{TeXLive 2021} ali \texttt{TeXLive 2020}.} +izvorna koda, zgodovina sprememb in prejšnje različice, je na voljo v mojem šolskem Git repozitoriju na +\url{https://git.sijanec.eu/sijanec/sola-gimb-2} v mapi +\href{https://git.sijanec/sola-gimb-2/src/branch/master/\predmdn/\predmkaj/\stevilkadn/}{/\predmdn/\predmkaj/\stevilkadn/}. Povezava za ogled zadnje različice tega dokumenta v PDF obliki je \url{http://razor.arnes.si/~asija3/files/sola/gimb/2/\predmdn/\predmkaj/\stevilkadn/dokument.pdf} in/ali \url{https://git.sijanec.eu/sijanec/sola-gimb-2/raw/branch/master/\predmdn/\predmkaj/\stevilkadn/dokument.pdf}. +\if\razhroscevanje1 +\vfill +\section*{Razhroščevalne informacije} +Te informacije so generirane, ker je omogočeno razhroščevanje. Pred objavo dokumenta izklopite razhroščevanje. To naredite tako, da nastavite ukaz \texttt{razhroscevanje} na 0 v začetku dokumenta. + +Grafi imajo natančnost \functionSamples\space točk na graf. + +Konec generiranja dokumenta: \today\ ob \currenttime\footnote{To ne nakazuje dejanskega časa, ko je bil dokument napisan, temveč čas, ko je bi dokument generiran v PDF/DVI obliko. Isto velja za datum v glavi dokumenta. Če berete direktno iz LaTeX datoteke, bo to vedno današnji datum.}%\input|"date -Ins" + +Dokument se je generiral R0qK1KR2 \SI{}{\second}. +\fi +% \item $$$$ aaasecgeninsaaa R0qK1KR2 +\end{document} |