Grafici con Tikz numero 18

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Prima figura

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codice prima figura

\begin{tikzpicture}
\begin{axis}[
axis x line=center,
axis y line=center,
xmin = -0.5,
xmax = 13.5,
ymin = -0.5,
ymax = 9.5,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{-0.9cm}0$},
y label style={anchor=north east}
]

\addplot[azzurro, very thick,domain=0:12,samples=100,name path=bisettrice] {x};
\addplot[verdeforesta, very thick,domain=0:12,samples=100,name path=radice] {sqrt(5*x)};
\addplot[thin, samples=10,name path=asse,domain=-4:4] {0};
\addplot[mark=*] coordinates {(0.5,{sqrt(5/2)})} node[left] {$P_0$};
\addplot[mark=*] coordinates {({sqrt(5/2)},{(5^3/2)^(1/4)})} node[above left] {$P_1$};
\addplot[mark=*] coordinates {({(5^3/2)^(1/4)}, {(5^7/2)^(1/8)} )} node[above left] {$P_2$};
\addplot[mark=*] coordinates {({(5^7/2)^(1/8)}, {(5^(15)/2)^(1/16)})} node[above left] {$P_3$};
\addplot[mark=*] coordinates {({(5^(15)/2)^(1/16)}, {(5^(31)/2)^(1/32)})} node[above left] {$P_n$};

\addplot +[black, mark=none, name path=vert1] coordinates {(0.5,0) (0.5, {sqrt(5/2)})};
\addplot +[black, mark=none, name path=vert2] coordinates {({sqrt(5/2)},{sqrt(5/2)}) ({sqrt(5/2)}, {(5^3/2)^(1/4)})};
\addplot +[black, mark=none, dashed, name path=vert3] coordinates {({(5^3/2)^(1/4)},{(5^3/2)^(1/4)}) ({(5^3/2)^(1/4)}, {(5^7/2)^(1/8)})};
\addplot +[black, mark=none, dashed, name path=vert4] coordinates {({(5^7/2)^(1/8)},{(5^7/2)^(1/8)}) ({(5^7/2)^(1/8)}, {(5^(15)/2)^(1/16)})};
\addplot +[black, mark=none, dashed, name path=vert4] coordinates {({(5^(15)/2)^(1/16)},{(5^(15)/2)^(1/16)}) ({(5^(15)/2)^(1/16)}, {(5^(31)/2)^(1/32)})};

\addplot +[black, mark=none, dashed, name path=hor1] coordinates {(0.5,{sqrt(5/2)}) ({sqrt(5/2)}, {sqrt(5/2)})};
\addplot +[black, mark=none, dashed, name path=hor2] coordinates {({sqrt(5/2)},{(5^3/2)^(1/4)}) ({(5^3/2)^(1/4)}, {(5^3/2)^(1/4)})};
\addplot +[black, mark=none, dashed, name path=hor3] coordinates {({(5^3/2)^(1/4)},{(5^7/2)^(1/8)}) ({(5^7/2)^(1/8)}, {(5^7/2)^(1/8)})};
\addplot +[black, mark=none, dashed, name path=hor4] coordinates {({(5^7/2)^(1/8)},{(5^(15)/2)^(1/16)}) ({(5^(15)/2)^(1/16)}, {(5^(15)/2)^(1/16)})};

\end{axis}
\end{tikzpicture}

seconda figura

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codice seconda figura

\begin{tikzpicture}
\begin{axis}[
axis x line=center,
axis y line=center,
xmin = -1.5,
xmax = 13.5,
ymin = -0.5,
ymax = 9.5,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{-0.9cm}0$},
y label style={anchor=north east}
]

\addplot[red, very thick,domain=0:12,samples=100,name path=bisettrice] {x};
\addplot[azzurro, very thick,domain=(-1.2:12),samples=400,name path=radice] {sqrt(5*x+6)};
\addplot[mark=*] coordinates {(2,4)} node[left] {$P_0$};
\addplot[mark=*] coordinates {(4,5.1)} node[above left] {$P_1$};
\addplot[mark=*] coordinates {(5.1, 5.6)} node[above left] {$P_2$};
\addplot[mark=*] coordinates {(5.6, 5.8)} node[above left] {$P_3$};

\addplot[mark=*] coordinates {(4,4)} node[below right] {$Q_0$};
\addplot[mark=*] coordinates {(5.1,5.1)} node[below right] {$Q_1$};
\addplot[mark=*] coordinates {(5.6,5.6)} node[below right] {$Q_2$};

\addplot +[black, mark=none, name path=vert1] coordinates {(2,0) (2,4)};
\addplot +[black, mark=none, dashed, name path=vert2] coordinates {(4,4) (4,5.1)};
\addplot +[black, mark=none, dashed, name path=vert3] coordinates {(5.1,5.1) (5.1, 5.6)};
\addplot +[black, mark=none, dashed, name path=vert4] coordinates {(5.6,5.6) (5.6, 5.8)};

\addplot +[black, mark=none, dashed, name path=hor1] coordinates {(2,4) (4, 4)};
\addplot +[black, mark=none, dashed, name path=hor2] coordinates {(4,5.1) (5.1, 5.1)};
\addplot +[black, mark=none, dashed, name path=hor3] coordinates {(5.1,5.6) (5.6, 5.6)};

\end{axis}
\end{tikzpicture}

terza figura

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codice terza figura

\begin{tikzpicture}
\begin{axis}[
axis x line=center,
axis y line=center,
xmin = -1.5,
xmax = 12.5,
ymin = -0.5,
ymax = 9.5,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{-0.9cm}0$},
y label style={anchor=north east}
]

\addplot[azzurro, very thick,domain=0:12,samples=100,name path=bisettrice] {x};
\addplot[verdeforesta, very thick,domain=(-1.2:12),samples=400,name path=radice] {sqrt(5*x+6)};
\addplot[mark=*] coordinates {(10,7.48)} node[above] {$P_0$};
\addplot[mark=*] coordinates {(7.48,6.59)} node[below right] {$P_1$};
\addplot[mark=*] coordinates {(6.69, 6.24)} node[below right] {$P_2$};

\addplot[mark=*] coordinates {({sqrt(56)},{sqrt(56)})} node[above] {$Q_0$};
\addplot[mark=*] coordinates {(6.59,6.59)} node[above] {$Q_1$};
\addplot[mark=*] coordinates {(6.24,6.24)} node[left] {$Q_2$};

\addplot +[black, mark=none, name path=vert1] coordinates {(10,0) (10,7.48)};
\addplot +[black, mark=none, dashed, name path=vert2] coordinates {(7.48,6.59) (7.48,{sqrt(56)})};
\addplot +[black, mark=none, dashed, name path=vert3] coordinates {(6.59,6.24) (6.59, 6.59)};
\addplot +[black, mark=none, dashed, name path=vert4] coordinates {(5.6,5.6) (5.6, 5.8)};

\addplot +[black, mark=none, dashed, name path=hor1] coordinates {(10,7.48) ({sqrt(56)}, {sqrt(56)})};
\addplot +[black, mark=none, dashed, name path=hor2] coordinates {(7.48,6.59) (6.59, 6.59)};

\end{axis}
\end{tikzpicture}