Plots used in Stewart's Calculus books

Question

I'm trying to recreate some diagrams and graphs on Stewart's Calculus book. I've seen this topic but they didn't explain how to create the top left plot, the one I'm aiming to recreate. To begin with I'm trying this one

but all my attempts using TikZ have been miserably failed. Any ideas?

Answer 1

This should give you a good starting point. To plot the square root, I chose to plot x² against x instead of x against sqrt(x), because the precision of the square root calculation in TeX is not very good and also takes a long time.

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[x={(-1.3cm,-1.3cm)},y={(2.7cm,-.3cm)},z={(0cm,2cm)}]
  \draw[->] (0,0,0) -- (1.5,0,0) node[left] {$x$};
  \draw[dashed] (0,0,0) -- (0,1,0);
  \draw[->] (0,1,0) -- (0,1.5,0) node[below] {$y$};
  \draw[->] (0,0,0) -- (0,0,1.5) node[left] {$z$};
  \draw[thick,cyan] (0,0,0)
    -- plot[domain=0:1] ({\x*\x},{\x},{0})
    -- plot[domain=1:0] ({\x*\x},{\x},{1-\x});
  \fill[cyan,opacity=.2] (0,0,0)
    -- plot[domain=0:1] ({\x*\x},{\x},{0})
    -- plot[domain=1:0] ({\x*\x},{\x},{1-\x});
    -- cycle;
  \draw[thick,cyan] (0,0,1)
    -- plot[domain=0:1] ({\x*\x},{\x},{1-\x})
    -- (0,1,0)
    -- cycle;
  \fill[cyan,opacity=.2] (0,0,1)
    -- plot[domain=0:1] ({\x*\x},{\x},{1-\x})
    -- (0,1,0)
    -- cycle;
\end{tikzpicture}
\end{document}