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如何在 LaTeX 中绘制极限的下一个图形示例？

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如何在 LaTeX 中绘制极限的下一个图形示例？

如何在 LaTeX 中绘制极限的下一个图形示例？

例 1. 极限的图形 例2. 极限的图形

答案1

如果你想在LaTeX，您可以使用 TikZ 和 PGF，手册可以在这里找到：http://ctan.sharelatex.com/tex-archive/graphics/pgf/base/doc/generic/pgf/pgfmanual.pdf

PSTricks 文档可以在这里找到：https://www.tug.org/PSTricks/main.cgi?file=doc/docs

PGFplots手册可以在这里找到：http://pgfplots.sourceforge.net/pgfplots.pdf

感谢亚历山大指出该PGFplots手册的更新版本。

根据 texenthusiat 的评论，您也可以使用texdoc pgf pgfplots pstricks它TeXLive来获取手册。

要绘制抛物线，您可以执行以下操作（PGFplots）：

\documentclass[tikz, convert = false]{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}
  \addplot[blue] plot[domain = -2:4, samples = 100] (x, 3 * x * x);
\end{axis}
\end{tikzpicture}
\end{document}

在此处输入图片描述

\documentclass[tikz, convert = false]{standalone}
\begin{document}
\begin{tikzpicture}
  \draw[blue] plot[domain = -2:4, samples = 100] ({\x}, {3 * (\x)^2});
\end{tikzpicture}
\end{document}

在此处输入图片描述

我不会为你画出每幅图，但这里是用两种方法画出抛物线的。

这是第一个限制示例：

\documentclass[tikz, convert = false]{standalone}
\begin{document}
\begin{tikzpicture}[xscale = 5]
  \clip (1.25, 8.75) rectangle (2.8, 15);
  \draw[-latex] (1.5, 9) -- (1.5, 15);
  \draw[-latex] (1.5, 9) -- (2.75, 9);

  \foreach \y in {9, 10, ..., 14}{
    \node[left, font = \tiny] at (1.5, \y) {\y};
    \draw (1.5, \y) -- +(.02, 0);
  }

  \foreach \x in {1.6, 1.8, ..., 2.4}{
    \node[below, font = \tiny] at (\x, 9) {\x};
    \draw (\x, 9) -- +(0, .08);
  }
  \draw[blue] plot[domain = 1.5:2.25, samples = 100] ({\x}, {3 *(\x)^2});
  \draw (1.5, 12.05) -- (2.4, 12.05) node[above, blue, font = \tiny, pos = .2]
  {\(y = 12.05\)};
  \draw (1.5, 11.95) -- (2.4, 11.95) node[below, blue, font = \tiny, pos = .2]
  {\(y = 11.95\)};

  \node[font = \tiny, right, blue] at (2.2, 14) {\(y = 3x^2\)};
\end{tikzpicture}
\end{document}

在此处输入图片描述

因为我很无聊，不想做自己的工作：

\documentclass[convert = false, tikz]{standalone}
\usetikzlibrary{intersections}
\usetikzlibrary{backgrounds}
\begin{document}
\begin{tikzpicture}%[xscale = 2]                                                    
  %\coordinate (O) at (0, 0);                                                       

  \draw[-latex, name path = xline] (-.5, 0) -- (2, 0) node[right, font = \tiny]
  {x};
  \draw[-latex] (0, -.2) -- (0, 4.5) node[right, font = \tiny] {y};
  \draw (1, .05) -- (1, -.05) node[below, font = \tiny] {1};
  \draw[-stealth] (-.6, 3.9) -- (-.6, 3.1) node[pos = -.15, font = \tiny]
  {$f(x)$};
  \draw[-stealth] (-.6, 2.1) -- (-.6, 2.9) node[pos = -.15, font = \tiny]
  {$f(x)$};
  \draw[-stealth] (.6, -.3) -- (.9, -.3) node[pos = -.2, font = \tiny]
  {$x$};
  \draw[-stealth] (1.4, -.3) -- (1.1, -.3) node[pos = -.2, font = \tiny]
  {$x$};

  \foreach \y in {1, 2, 3, 4}{
    \draw (.05, \y) -- (-.05, \y) node[left, font = \tiny] {\y};
  }

  \draw[blue!40, name path = para] plot[domain = -.1:1.3, samples = 100]
  ({\x}, {2 * (\x)^2 + 1});
  \draw[blue!40, fill = white] (1, 3) circle[radius = .02cm];

  \begin{scope}[on background layer]
    \foreach \yl/\i in {2.1/1, 2.4/2, 2.55/3, 2.8/4, 2.9/5}{

      \filldraw[black] (0, \yl) circle[radius = .02cm];

      \path[name path global = \i] (0, \yl) -- +(2, 0);
      \path[name intersections = {of = para and \i, by = P\i}];

      \draw (0, \yl) -- (P\i);

      \begin{pgfinterruptboundingbox}
        \path[name path global = Pxl\i] (P\i) -- +(0, -5);
      \end{pgfinterruptboundingbox}

      \path[name intersections = {of = xline and Pxl\i, by = Xl\i}];

      \draw (P\i) -- (Xl\i);

      \filldraw[black] (Xl\i) circle[radius = .02cm];
    }

    \foreach \yu/\i in {4.1/6, 3.6/7, 3.45/8, 3.2/9, 3.1/10}{
      \filldraw[black] (0, \yu) circle[radius = .02cm];

      \path[name path global = \i] (0, \yu) -- +(2, 0);
      \path[name intersections = {of = para and \i, by = P\i}];

      \draw (0, \yu) -- (P\i);

      \begin{pgfinterruptboundingbox}
        \path[name path global = Pxu\i] (P\i) -- +(0, -5);
      \end{pgfinterruptboundingbox}

      \path[name intersections = {of = xline and Pxu\i, by = Xu\i}];

      \draw (P\i) -- (Xu\i);

      \filldraw[black] (Xu\i) circle[radius = .02cm];
    }
  \end{scope}
\end{tikzpicture}
\end{document}

在此处输入图片描述

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