-#LyX 1.6.5 created this file. For more info see http://www.lyx.org/
-\lyxformat 345
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
\begin_document
\begin_header
\textclass tufte-book
\end_preamble
\options noindentfirst
\use_default_options true
+\maintain_unincluded_children false
\language spanish
+\language_package default
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\cite_engine basic
\use_bibtopic false
+\use_indices false
\paperorientation portrait
+\suppress_date false
+\use_refstyle 0
+\index Índice
+\shortcut idx
+\color #008000
+\end_index
\secnumdepth 2
\tocdepth 2
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+\paragraph_indentation default
\quotes_language english
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-\author ""
-\author ""
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\end_header
\begin_body
+\begin_layout Standard
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+\lang english
+Note
+\series default
+: To be able to view your file as PDF you must have the LaTeX-package
+\family sans
+fpl
+\family default
+ installed to your LaTeX system.
+ If you are using MiKTeX, you will automatically be asked to install this
+ package when previewing your file, if you are using TeXLive, use TeXLive's
+ package manager.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
\begin_layout Title
Ejemplos Tufte
\end_layout
has_inner_box 1
inner_pos "t"
use_parbox 0
+use_makebox 0
width "100col%"
special "none"
height "1in"
has_inner_box 1
inner_pos "t"
use_parbox 0
+use_makebox 0
width "100col%"
special "none"
height "1in"
has_inner_box 1
inner_pos "t"
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width "100line%"
special "none"
height "1in"
has_inner_box 1
inner_pos "t"
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width "100col%"
special "none"
height "1in"
has_inner_box 1
inner_pos "t"
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+use_makebox 0
width "100col%"
special "none"
height "1in"
Después, podemos encontrar el volumen de cada cilindro/disco.
La fórmula básica es:
-\begin_inset Formula \[
-V=hA\]
+\begin_inset Formula
+\[
+V=hA
+\]
\end_inset
.
Por sustitución
-\begin_inset Formula \[
-A=\pi f^{2}(x)\]
+\begin_inset Formula
+\[
+A=\pi f^{2}(x)
+\]
\end_inset
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula
+\begin{eqnarray*}
A & = & \pi\left(\sqrt{x}\right)^{2}\\
- & = & \pi x\end{eqnarray*}
+ & = & \pi x
+\end{eqnarray*}
\end_inset
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-V=\pi x\, dx\]
+\begin_inset Formula
+\[
+V=\pi x\, dx
+\]
\end_inset
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
-V=\pi f^{2}(x)\, dx\]
+\begin_inset Formula
+\[
+V=\pi f^{2}(x)\, dx
+\]
\end_inset
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{equation}
-\int_{a}^{b}\,\pi f^{2}(x)\, dx\end{equation}
+\begin_inset Formula
+\begin{equation}
+\int_{a}^{b}\,\pi f^{2}(x)\, dx
+\end{equation}
\end_inset
\end_inset
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula
+\begin{eqnarray*}
\int_{0}^{4}\,\pi x\, dx & = & \pi\int_{0}^{4}\, x\, dx\\
& = & \pi\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}\\
& = & \pi\left(\frac{4^{2}}{2}-0\right)\\
- & = & 8\pi\end{eqnarray*}
+ & = & 8\pi
+\end{eqnarray*}
\end_inset
has_inner_box 1
inner_pos "t"
use_parbox 0
+use_makebox 0
width "100col%"
special "none"
height "1in"
\end_inset
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula
+\begin{eqnarray*}
A_{arandela} & = & A_{copa}-A_{taladro}\\
& = & \pi f^{2}(x)-\pi g^{2}(x)\\
- & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\end{eqnarray*}
+ & = & \pi\left(f^{2}(x)-g^{2}(x)\right)
+\end{eqnarray*}
\end_inset
El volumen de cada arandela sería
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula
+\begin{eqnarray*}
V_{arandela} & = & A_{arandela}\, dx\\
- & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\, dx\end{eqnarray*}
+ & = & \pi\left(f^{2}(x)-g^{2}(x)\right)\, dx
+\end{eqnarray*}
\end_inset
\end_inset
, se obtiene la integral:
-\begin_inset Formula \begin{equation}
-\int_{a}^{b}\,\pi\left(f^{2}(x)-g^{2}(x)\right)\, dx\end{equation}
+\begin_inset Formula
+\begin{equation}
+\int_{a}^{b}\,\pi\left(f^{2}(x)-g^{2}(x)\right)\, dx
+\end{equation}
\end_inset
has_inner_box 1
inner_pos "t"
use_parbox 0
+use_makebox 0
width "100col%"
special "none"
height "1in"
\end_inset
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula
+\begin{eqnarray*}
\int_{0}^{4}\,\pi\left(\left(\sqrt{x}\right)^{2}-\left(\frac{x^{2}}{16}\right)\right)\, dx & = & \pi\int_{0}^{4}\,\left(x-\frac{x^{4}}{256}\right)\, dx\\
& = & \pi\left(\int_{0}^{4}\, x\, dx-\int_{0}^{4}\,\frac{x^{4}}{256}\, dx\right)\\
& = & \pi\left(\left.\left(\frac{x^{2}}{2}\right)\right|_{0}^{4}-\left.\left(\frac{x^{5}}{1280}\right)\right|_{0}^{4}\right)\\
& = & \pi\left(\left(\frac{4^{2}}{2}-0\right)-\left(\frac{4^{5}}{1280}-0\right)\right)\\
& = & \pi\left(8-0.8\right)\\
- & = & 7.2\pi\end{eqnarray*}
+ & = & 7.2\pi
+\end{eqnarray*}
\end_inset
projects / lyx.git / blobdiff