Draw mathematical analysis figures in latex

Question

I wonder if it is possible to draw the following figures in latex:

For the first image I want a typical real analysis diagram. For the other three I want to draw a cylinder and with squares and rhombus sections...

Is this possible with latex?

Ŕeferences

For my own reference I save here some examples of tikz referenced in the comments:

http://www.texample.net/tikz/examples/

Answer 1

\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\tdplotsetmaincoords{0}{0}
\begin{document}

\begin{tikzpicture}[thick]
 \draw[-latex](-1,0)--(6,0);
 \draw[-latex](0,-1)--(0,4);
 \coordinate (O) at (0,0);
 \coordinate (lb) at (1,1);
 \coordinate (tr) at (5,3);
 \draw (lb) rectangle (tr);
 \coordinate (x) at (barycentric cs:lb=1,tr=1);
 \draw[fill] (x) circle (2pt);
 \draw[dashed] (lb) -- (O-|lb) node[below] {$t_0-a$};
 \draw[dashed] (lb-|tr) -- (O-|tr) node[below] {$t_0+a$};
 \draw[dashed] (lb) -- (O|-lb) node[left] {$x_0-b$};
 \draw[dashed] (lb|-tr) -- (O|-tr) node[left] {$x_0+b$};
 \draw[dashed] (lb-|x) -- (O-|x) node[below] {$t_0$};
 \draw[dashed] (lb|-x) -- (O|-x) node[left] {$x_0$};
\end{tikzpicture}

\begin{tikzpicture}[thick]
\tdplotsetrotatedcoords{0}{70}{0}
\begin{scope}[tdplot_rotated_coords]
\foreach \X in {0,3,6}
{
\ifnum\X=0
\draw (0,0,\X) circle (1);
\else
\draw (0,-1,\X) arc[radius=1,start angle=-90,end angle=90];
\draw[dashed] (0,-1,\X) arc[radius=1,start angle=-90,end angle=-270];
\fi
}
\draw (0,1,0) -- (0,1,6);
\draw (0,-1,0) -- (0,-1,6);
\end{scope}
\end{tikzpicture}


\begin{tikzpicture}[thick]
\tdplotsetrotatedcoords{0}{70}{-20}
\begin{scope}[tdplot_rotated_coords]
\foreach \X in {0,3,6}
{\ifnum\X=0
\draw (-1.5,-1,\X) -- (-1.5,1,\X) -- (1.5,1,\X) -- (1.5,-1,\X) -- cycle;
\else
\draw[dashed] (-1.5,1,\X) -- (-1.5,-1,\X) -- (1.5,-1,\X);
\draw (-1.5,1,\X) -- (1.5,1,\X) -- (1.5,-1,\X);
\fi
}
\draw[dashed] (-1.5,-1,0) -- (-1.5,-1,6);
\draw (-1.5,1,0) -- (-1.5,1,6);
\draw (1.5,-1,0) -- (1.5,-1,6);
\draw (1.5,1,0) -- (1.5,1,6);
\end{scope}
\end{tikzpicture}

\begin{tikzpicture}[thick]
\tdplotsetrotatedcoords{0}{110}{-70}
\begin{scope}[tdplot_rotated_coords]
\foreach \X in {0,3,6}
{\ifnum\X=0
\draw (-1.5,-1,\X) -- (-1.5,1,\X) -- (1.5,1,\X) -- (1.5,-1,\X) -- cycle;
\else
\draw[dashed] (-1.5,1,\X) -- (1.5,1,\X) -- (1.5,-1,\X);
\draw (-1.5,1,\X) -- (-1.5,-1,\X) -- (1.5,-1,\X);
\fi
}
\draw (-1.5,-1,0) -- (-1.5,-1,6);
\draw (-1.5,1,0) -- (-1.5,1,6);
\draw (1.5,-1,0) -- (1.5,-1,6);
\draw[dashed] (1.5,1,0) -- (1.5,1,6);
\end{scope}
\end{tikzpicture}
\end{document}