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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. 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Consider writing \pgfplotsset{compat=1.17} into +your preamble. + on input line 134. + + +(/usr/local/texlive/2021/texmf-dist/tex/latex/siunitx/siunitx-abbreviations.cfg +) +(/usr/local/texlive/2021/texmf-dist/tex/latex/translator/translator-basic-dicti +onary-English.dict) +(/usr/local/texlive/2021/texmf-dist/tex/latex/exsheets/exsheets_configurations. +cfg) (/usr/local/texlive/2021/texmf-dist/tex/latex/amsfonts/umsa.fd) +(/usr/local/texlive/2021/texmf-dist/tex/latex/amsfonts/umsb.fd) [1{/usr/local/t +exlive/2021/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] [2] [3] [4] +(./dokument.aux) ) +(see the transcript file for additional information) +Output written on dokument.pdf (4 pages, 286793 bytes). +SyncTeX written on dokument.synctex.gz. +Transcript written on dokument.log. +Reading 1 0 R +Reading 2 0 R +Reading 3 0 R +Reading 4 0 R +-> Uncompressing object 4 0 +-> Original Length: 15 +-> Uncompressed Length: 7 +Reading 5 0 R +Reading 7 0 R +-> Uncompressing object 7 0 +-> Original 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This may have been caused + **** by a problem while converting or transfering the file. + **** Ghostscript will attempt to recover the data. + **** However, the output may be incorrect. + **** Error: stream Length incorrect. + Output may be incorrect. -- cgit v1.2.3