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\documentclass{article} \usepackage{tikz} \usepackage{tikz-3dplot} \usetikzlibrary{math} \usepackage{ifthen} \usepackage[active,tightpage]{preview} \PreviewEnvironment{tikzpicture} \setlength\PreviewBorder{1pt} % % File name: derivative-vector-function.tex % Description: % A geometric representation of the steps one and two used % (from the four step rule) % to compute the derivative of a vector function is shown. % % Date of creation: October, 10th, 2021. % Date of last modification: October, 9th, 2022. % Author: Efraín Soto Apolinar. % https://www.aprendematematicas.org.mx/author/efrain-soto-apolinar/instructing-courses/ % Source: page 211 of the % Glosario Ilustrado de Matem\'aticas Escolares. % https://tinyurl.com/5udm2ufy % % Terms of use: % According to TikZ.net % https://creativecommons.org/licenses/by-nc-sa/4.0/ % Your commitment to the terms of use is greatly appreciated. % \begin{document} % \begin{center} \tdplotsetmaincoords{70}{120} % \begin{tikzpicture}[tdplot_main_coords,scale=1.0] % Component functions of the vector function \tikzmath{function equis(\t) {return cos((\t) r);};} \tikzmath{function ye(\t) {return sin((\t) r);};} \tikzmath{function zeta(\t) {return 0.25+sqrt(\t);};} % Evaluated at $t = \ti$ \pgfmathsetmacro{\ti}{0.25} \pgfmathsetmacro{\tf}{2*pi} \pgfmathsetmacro{\n}{10} \pgfmathsetmacro{\r}{2.0} \pgfmathsetmacro{\step}{(\tf-\ti)/\n} \pgfmathsetmacro{\tcero}{0.8*pi} \pgfmathsetmacro{\tuno}{\tcero+\step} % \pgfmathsetmacro{\xi}{\r*equis(\ti)} \pgfmathsetmacro{\xf}{\r*equis(\tf)} \pgfmathsetmacro{\xtcero}{\r*equis(\tcero)} \pgfmathsetmacro{\xtuno}{\r*equis(\tuno)} \pgfmathsetmacro{\yi}{\r*ye(\ti)} \pgfmathsetmacro{\yf}{\r*ye(\tf)} \pgfmathsetmacro{\ytcero}{\r*ye(\tcero)} \pgfmathsetmacro{\ytuno}{\r*ye(\tuno)} \pgfmathsetmacro{\zi}{\r*zeta(\ti)} \pgfmathsetmacro{\zf}{\r*zeta(\tf)} \pgfmathsetmacro{\ztcero}{\r*zeta(\tcero)} \pgfmathsetmacro{\ztuno}{\r*zeta(\tuno)} % Coordinate axis \draw[thick,->] (-1.25,0,0) -- (1.5,0,0) node[below left] {$x$}; % Eje x \foreach \x in {-1,1} \draw[thick] (\x,0,0.05) -- (\x,0,-0.05) node [below] {$\x$}; \draw[thick,->] (0,-1.25,0) -- (0,1.5,0) node[right] {$y$}; % Eje y \foreach \y in {-1,1} \draw[thick] (0,\y,0.05) -- (0,\y,-0.05) node [below] {$\y$}; \draw[thick] (0,0,-0.25) -- (0,0,0.75); % Eje z (Primera parte) % Graph of the function $\vec{r}(t)$ \draw[red,thick,->] plot[domain=\ti:\tf,smooth,variable=\t] ({\r*equis(\t)},{\r*ye(\t)},{\r*zeta(\t)}); \node[red,above] at (\xf,\yf,\zf+0.25) {$\vec{r(t)}$}; % $z$ axis \draw[thick,->] (0,0,0.75) -- (0,0,\zf+0.5) node[above] {$z$}; % Eje z \foreach \z/\posicion in {1/left} \draw[thick] (0,0.05,\z) -- (0,-0.05,\z) node [\posicion] {$\z$}; % Node $\vec{r}(t)$ \draw[blue,thick,->] (0,0,0) -- (\xtcero,\ytcero,\ztcero) node[sloped,below,near end] {\footnotesize$\vec{r}(t)$}; % Node $\vec{r}(t + \Delta t)$ \draw[blue,thick,->] (0,0,0) -- (\xtuno,\ytuno,\ztuno) node[sloped,above,near end] {\footnotesize$\vec{r}(t + \Delta t)$}; % Node $\Delta r$ \draw[blue,thick,->] (\xtcero,\ytcero,\ztcero) -- (\xtuno,\ytuno,\ztuno) node[midway,sloped,above] {\footnotesize$\Delta\vec{r}$}; \end{tikzpicture} \end{center} % \end{document}
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