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Undo xml:id splitting
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@sean-fitzpatrick
sean-fitzpatrick committed Jul 18, 2024
1 parent 96d713b commit b6e8ee3
Showing 1 changed file with 14 additions and 32 deletions.
46 changes: 14 additions & 32 deletions ptx/sec_taylor_poly.ptx
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Original file line number Diff line number Diff line change
Expand Up @@ -428,12 +428,12 @@
</p>
</aside>

<figure xml:id="vid_deriv_apps_taylor_poly_defn-early" component="video-early" vshift="-3">
<figure xml:id="vid_deriv_apps_taylor_poly_defn" component="video-early" vshift="-3">
<caption>Video presentation of <xref ref="def_taypoly"/></caption>
<video youtube="J-5vVJIGQp4" label="vid_deriv_apps_taylor_poly_defn"/>
</figure>

<figure xml:id="vid_deriv_apps_taylor_poly_defn-late" component="video-late" vshift="1">
<figure xml:id="vid_deriv_apps_taylor_poly_defn" component="video-late" vshift="1">
<caption>Video presentation of <xref ref="def_taypoly"/></caption>
<video youtube="J-5vVJIGQp4" label="vid_deriv_apps_taylor_poly_defn"/>
</figure>
Expand Down Expand Up @@ -1094,21 +1094,14 @@
Thus we want to approximate <m>\cos(2)</m> with <m>p_9(2)</m>.
</p>

<p component="taypoly-early">
We now set out to compute <m>p_9(x)</m>.
We again need a table of the derivatives of
<m>f(x)=\cos(x)</m> evaluated at <m>x=0</m>.
A table of these values is given in <xref ref="fig_taypoly4a-early"/>.
</p>

<p component="taypoly-late">
<p>
We now set out to compute <m>p_9(x)</m>.
We again need a table of the derivatives of
<m>f(x)=\cos(x)</m> evaluated at <m>x=0</m>.
A table of these values is given in <xref ref="fig_taypoly4a-late"/>.
A table of these values is given in <xref ref="fig_taypoly4a"/>.
</p>

<figure xml:id="fig_taypoly4a-late" vshift="4" component="taypoly-late">
<figure xml:id="fig_taypoly4a" vshift="4" component="taypoly-late">
<caption>A table of the derivatives of <m>f(x)=\cos(x)</m> evaluated at <m>x=0</m></caption>
<tabular>
<row>
Expand Down Expand Up @@ -1154,7 +1147,7 @@
</tabular>
</figure>

<figure xml:id="fig_taypoly4a-early" vshift="0" component="taypoly-early">
<figure xml:id="fig_taypoly4a" vshift="0" component="taypoly-early">
<caption>A table of the derivatives of <m>f(x)=\cos(x)</m> evaluated at <m>x=0</m></caption>
<tabular>
<row>
Expand Down Expand Up @@ -1231,19 +1224,13 @@
<m>0.0003</m> of the correct answer.
</p>

<p component="taypoly-late">
<xref ref="fig_taypoly4b-late"/>
shows a graph of <m>y=p_8(x)</m> and <m>y=\cos(x)</m>.
Note how well the two functions agree on about <m>(-\pi,\pi)</m>.
</p>

<p component="taypoly-early">
<xref ref="fig_taypoly4b-early"/>
<p>
<xref ref="fig_taypoly4b"/>
shows a graph of <m>y=p_8(x)</m> and <m>y=\cos(x)</m>.
Note how well the two functions agree on about <m>(-\pi,\pi)</m>.
</p>

<figure xml:id="fig_taypoly4b-late" vshift="1" component="taypoly-late">
<figure xml:id="fig_taypoly4b" vshift="1" component="taypoly-late">
<caption>A graph of <m>f(x)= \cos(x)</m> and its degree 8 Maclaurin
polynomial</caption>
<!-- START figures/fig_taypoly4.tex -->
Expand Down Expand Up @@ -1292,7 +1279,7 @@
<!-- figures/fig_taypoly4.tex END -->
</figure>

<figure xml:id="fig_taypoly4b-early" vshift="-3" component="taypoly-early">
<figure xml:id="fig_taypoly4b" vshift="-3" component="taypoly-early">
<caption>A graph of <m>f(x)= \cos(x)</m> and its degree 8 Maclaurin
polynomial</caption>
<!-- START figures/fig_taypoly4.tex -->
Expand Down Expand Up @@ -1383,17 +1370,12 @@
<p>
<ol>
<li>
<p component="taypoly-late">
We begin by evaluating the derivatives of <m>f</m> at <m>x=4</m>.
This is done in <xref ref="fig_taypoly5a-late"/>.
</p>

<p component="taypoly-early">
<p>
We begin by evaluating the derivatives of <m>f</m> at <m>x=4</m>.
This is done in <xref ref="fig_taypoly5a-early"/>.
This is done in <xref ref="fig_taypoly5a"/>.
</p>

<figure xml:id="fig_taypoly5a-late" vshift="0" component="taypoly-late">
<figure xml:id="fig_taypoly5a" vshift="0" component="taypoly-late">
<caption>A table of the derivatives of <m>f(x)=\sqrt{x}</m> evaluated at <m>x=4</m></caption>
<tabular>
<row>
Expand All @@ -1419,7 +1401,7 @@
</tabular>
</figure>

<figure xml:id="fig_taypoly5a-early" vshift="-4.5" component="taypoly-early">
<figure xml:id="fig_taypoly5a" vshift="-4.5" component="taypoly-early">
<caption>A table of the derivatives of <m>f(x)=\sqrt{x}</m> evaluated at <m>x=4</m></caption>
<tabular>
<row>
Expand Down

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