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Description fixes #318

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Description fixes #318

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b1a1abf
fix issue with curve style override
sean-fitzpatrick Oct 2, 2024
283ff8f
fix descriptions in Section 1.1
sean-fitzpatrick Oct 2, 2024
875224d
fix descriptions in 1.3 and 1.4
sean-fitzpatrick Oct 2, 2024
21afad1
Fix descriptions in 1.5 and 1.6
sean-fitzpatrick Oct 7, 2024
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60 changes: 30 additions & 30 deletions ptx/docinfo.ptx
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -163,21 +163,21 @@
\pgfplotsset{hollowdot/.style={color=firstcolor,fill=white,only marks,mark=*}}
\pgfplotsset{soliddot/.style={color=firstcolor,fill=firstcolor,only marks,mark=*}}

\pgfplotsset{open/.style={firstcurvestyle,shorten <=-2.4pt,shorten >=-2.4pt,{Circle[open]}-{Circle[open]}}}
\pgfplotsset{openclosed/.style={firstcurvestyle,shorten <=-2.4pt,shorten >=-2.4pt,{Circle[open]}-{Circle}}}
\pgfplotsset{closed/.style={firstcurvestyle,shorten <=-2.4pt,shorten >=-2.4pt,{Circle}-{Circle}}}
\pgfplotsset{closedopen/.style={firstcurvestyle,shorten <=-2.4pt,shorten >=-2.4pt,{Circle}-{Circle[open]}}}
\pgfplotsset{infiniteopen/.style={firstcurvestyle,shorten >=-2.4pt,{Kite}-{Circle[open]}}}
\pgfplotsset{openinfinite/.style={firstcurvestyle,shorten <=-2.4pt,{Circle[open]}-{Kite}}}
\pgfplotsset{infiniteclosed/.style={firstcurvestyle,shorten >=-2.4pt,{Kite}-{Circle}}}
\pgfplotsset{closedinfinite/.style={firstcurvestyle,shorten <=-2.4pt,{Circle}-{Kite}}}
\pgfplotsset{infinite/.style={firstcurvestyle,{Kite}-{Kite}}}
\pgfplotsset{infiniteleft/.style={firstcurvestyle,{Kite}-}}
\pgfplotsset{infiniteright/.style={firstcurvestyle,-{Kite}}}
\pgfplotsset{openleft/.style={firstcurvestyle,shorten <=-2.4pt,{Circle[open]}-}}
\pgfplotsset{openright/.style={firstcurvestyle,shorten >=-2.4pt,-{Circle[open]}}}
\pgfplotsset{closedleft/.style={firstcurvestyle,shorten <=-2.4pt,{Circle}-}}
\pgfplotsset{closedright/.style={firstcurvestyle,shorten >=-2.4pt,-{Circle}}}
\pgfplotsset{open/.style={shorten <=-2.4pt,shorten >=-2.4pt,{Circle[open]}-{Circle[open]}}}
\pgfplotsset{openclosed/.style={shorten <=-2.4pt,shorten >=-2.4pt,{Circle[open]}-{Circle}}}
\pgfplotsset{closed/.style={shorten <=-2.4pt,shorten >=-2.4pt,{Circle}-{Circle}}}
\pgfplotsset{closedopen/.style={shorten <=-2.4pt,shorten >=-2.4pt,{Circle}-{Circle[open]}}}
\pgfplotsset{infiniteopen/.style={shorten >=-2.4pt,{Kite}-{Circle[open]}}}
\pgfplotsset{openinfinite/.style={shorten <=-2.4pt,{Circle[open]}-{Kite}}}
\pgfplotsset{infiniteclosed/.style={shorten >=-2.4pt,{Kite}-{Circle}}}
\pgfplotsset{closedinfinite/.style={shorten <=-2.4pt,{Circle}-{Kite}}}
\pgfplotsset{infinite/.style={{Kite}-{Kite}}}
\pgfplotsset{infiniteleft/.style={{Kite}-}}
\pgfplotsset{infiniteright/.style={-{Kite}}}
\pgfplotsset{openleft/.style={shorten <=-2.4pt,{Circle[open]}-}}
\pgfplotsset{openright/.style={shorten >=-2.4pt,-{Circle[open]}}}
\pgfplotsset{closedleft/.style={shorten <=-2.4pt,{Circle}-}}
\pgfplotsset{closedright/.style={shorten >=-2.4pt,-{Circle}}}

\pgfplotsset{every axis/.append style = {
cycle list name = curvestylelist,
Expand Down Expand Up @@ -282,21 +282,21 @@
\pgfplotsset{hollowdot/.style={color=firstcolor,fill=white,only marks,mark size=2.4pt,mark=*}}
\pgfplotsset{soliddot/.style={color=firstcolor,fill=firstcolor,only marks,mark size=2.4pt,mark=*}}

\pgfplotsset{open/.style={firstcurvestyle,shorten <=-2.4pt,shorten >=-2.4pt,{Circle[open]}-{Circle[open]}}}
\pgfplotsset{openclosed/.style={firstcurvestyle,shorten <=-2.4pt,shorten >=-2.4pt,{Circle[open]}-{Circle}}}
\pgfplotsset{closed/.style={firstcurvestyle,shorten <=-2.4pt,shorten >=-2.4pt,{Circle}-{Circle}}}
\pgfplotsset{closedopen/.style={firstcurvestyle,shorten <=-2.4pt,shorten >=-2.4pt,{Circle}-{Circle[open]}}}
\pgfplotsset{infiniteopen/.style={firstcurvestyle,shorten >=-2.4pt,{Kite}-{Circle[open]}}}
\pgfplotsset{openinfinite/.style={firstcurvestyle,shorten <=-2.4pt,{Circle[open]}-{Kite}}}
\pgfplotsset{infiniteclosed/.style={firstcurvestyle,shorten >=-2.4pt,{Kite}-{Circle}}}
\pgfplotsset{closedinfinite/.style={firstcurvestyle,shorten <=-2.4pt,{Circle}-{Kite}}}
\pgfplotsset{infinite/.style={firstcurvestyle,{Kite}-{Kite}}}
\pgfplotsset{infiniteleft/.style={firstcurvestyle,{Kite}-}}
\pgfplotsset{infiniteright/.style={firstcurvestyle,-{Kite}}}
\pgfplotsset{openleft/.style={firstcurvestyle,shorten <=-2.4pt,{Circle[open]}-}}
\pgfplotsset{openright/.style={firstcurvestyle,shorten >=-2.4pt,-{Circle[open]}}}
\pgfplotsset{closedleft/.style={firstcurvestyle,shorten <=-2.4pt,{Circle}-}}
\pgfplotsset{closedright/.style={firstcurvestyle,shorten >=-2.4pt,-{Circle}}}
\pgfplotsset{open/.style={shorten <=-2.4pt,shorten >=-2.4pt,{Circle[open]}-{Circle[open]}}}
\pgfplotsset{openclosed/.style={shorten <=-2.4pt,shorten >=-2.4pt,{Circle[open]}-{Circle}}}
\pgfplotsset{closed/.style={shorten <=-2.4pt,shorten >=-2.4pt,{Circle}-{Circle}}}
\pgfplotsset{closedopen/.style={shorten <=-2.4pt,shorten >=-2.4pt,{Circle}-{Circle[open]}}}
\pgfplotsset{infiniteopen/.style={shorten >=-2.4pt,{Kite}-{Circle[open]}}}
\pgfplotsset{openinfinite/.style={shorten <=-2.4pt,{Circle[open]}-{Kite}}}
\pgfplotsset{infiniteclosed/.style={shorten >=-2.4pt,{Kite}-{Circle}}}
\pgfplotsset{closedinfinite/.style={shorten <=-2.4pt,{Circle}-{Kite}}}
\pgfplotsset{infinite/.style={{Kite}-{Kite}}}
\pgfplotsset{infiniteleft/.style={{Kite}-}}
\pgfplotsset{infiniteright/.style={-{Kite}}}
\pgfplotsset{openleft/.style={shorten <=-2.4pt,{Circle[open]}-}}
\pgfplotsset{openright/.style={shorten >=-2.4pt,-{Circle[open]}}}
\pgfplotsset{closedleft/.style={shorten <=-2.4pt,{Circle}-}}
\pgfplotsset{closedright/.style={shorten >=-2.4pt,-{Circle}}}

\pgfplotsset{every axis/.append style = {
cycle list name = curvestylelist,
Expand Down
14 changes: 7 additions & 7 deletions ptx/sec_alt_series.ptx
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Original file line number Diff line number Diff line change
Expand Up @@ -211,13 +211,13 @@
x post scale=2,
]

\addplot[infiniteright,domain=0:1] ({x},{2}) node [pos=1, right] {$a_1$};
\addplot[infiniteleft,domain=0.333:1] ({x},{1.75}) node [pos=0, left] {$-a_2$};
\addplot[infiniteright,domain=0.333:.833] ({x},{1.5}) node [pos=1, right] {$a_3$};
\addplot[infiniteleft,domain=0.433:.8333] ({x},{1.25}) node [pos=0, left] {$-a_4$};
\addplot[infiniteright,domain=0.4333:.76667] ({x},{1}) node [pos=1, right] {$a_5$};
\addplot[infiniteleft,domain=0.4809:.76667] ({x},{.75}) node [pos=0, left] {$-a_6$};
\addplot[infiniteright,domain=0.4809:.7309] ({x},{.5}) node [pos=1, right] {$a_7$};
\addplot[firstcurvestyle,infiniteright,domain=0:1] ({x},{2}) node [pos=1, right] {$a_1$};
\addplot[firstcurvestyle,infiniteleft,domain=0.333:1] ({x},{1.75}) node [pos=0, left] {$-a_2$};
\addplot[firstcurvestyle,infiniteright,domain=0.333:.833] ({x},{1.5}) node [pos=1, right] {$a_3$};
\addplot[firstcurvestyle,infiniteleft,domain=0.433:.8333] ({x},{1.25}) node [pos=0, left] {$-a_4$};
\addplot[firstcurvestyle,infiniteright,domain=0.4333:.76667] ({x},{1}) node [pos=1, right] {$a_5$};
\addplot[firstcurvestyle,infiniteleft,domain=0.4809:.76667] ({x},{.75}) node [pos=0, left] {$-a_6$};
\addplot[firstcurvestyle,infiniteright,domain=0.4809:.7309] ({x},{.5}) node [pos=1, right] {$a_7$};

\end{axis}

Expand Down
18 changes: 9 additions & 9 deletions ptx/sec_limit_analytically.ptx
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Original file line number Diff line number Diff line change
Expand Up @@ -483,19 +483,19 @@
<image width="47%">
<description>
<p>
Graph illustrating the squeeze theorem. There are three functions, <m>h(x)</m>,
An illustration of the squeeze theorem. There are graphs of three functions shown, labelled <m>h(x)</m>,
<m>g(x)</m>, and <m>f(x)</m>. On the <m>y</m>axis, there is a marker at <m>y = 4</m>,
labeled <m>L</m> and on the <m>x</m>axis there is a marker at <m>x = 5</m>, labeled
<m>c</m>.
</p>
<p>
For all values of <m>x \leq c</m> <m>f(x) \leq L</m> and <m>h(x) \geq L</m>.
For all values of <m>x</m> <m>f(x) \leq g(x) \leq h(x)</m>, that is, the line
of the function <m>g(x)</m> is between the lines of the functions <m>g(x)</m>
For all values of <m>x</m> <m>f(x) \leq g(x) \leq h(x)</m>, that is, the graph
of the function <m>g(x)</m> lies between the graphs of the functions <m>g(x)</m>
and <m>f(x)</m>.
</p>
<p>
The graph shows that where <m>x = c</m>, <m>f(x)</m> and <m>h(x)</m> converge
The image shows that where <m>x = c</m>, <m>f(x)</m> and <m>h(x)</m> converge
on <m>y = L = 4</m>. Because <m>f(x) \leq g(x) \leq h(x)</m>, we can extrapolate
that <m>\lim\limits_{x\to \c} g(x) = L</m> too.
</p>
Expand Down Expand Up @@ -953,15 +953,15 @@
<image width="47%">
<description>
<p>
Graph of the linear equation <m>(x^1-1)/(x-1)</m>, shows the function with
the <m>y</m> interval <m>0</m> to <m>3</m> and <m>x</m> interval <m>0</m>
to <m>2</m>. The function has a <m>y</m> intercept at <m>y = 1</m>, and
is undefined at <m>x = 1</m>. The graph has a positive slope.
Graph of the function <m>(x^2-1)/(x-1)</m>, showing the region with
<m>y</m> from <m>0</m> to <m>3</m> and <m>x</m> from <m>0</m>
to <m>2</m>. The graph is a straight line, with slope 1 and a <m>y</m> intercept at <m>y = 1</m>,
except for a hole at the point <m>(1,2)</m>, since the function is undefined at <m>x = 1</m>.
</p>
</description>
<shortdescription>
Graph of the polynomial x squared minus 1 divided by the polynomial x minus 1.
Is undefined at x = 1.
It is the same as the line y=x+1, except that it is undefined at x = 1.
</shortdescription>
<latex-image label="img_limitxplus1">
\begin{tikzpicture}
Expand Down
76 changes: 42 additions & 34 deletions ptx/sec_limit_continuity.ptx
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Expand Up @@ -105,14 +105,19 @@
<image width="47%">
<description>
<p>
Shows a graph with domain <m>0</m> to <m>3</m>. For <m>0 \geq x \lt 1</m>
the graph has a downward curve to it, for <m>1 &gt; x \leq 2</m> the graph
is a straight line, parallel with the <m>x</m> axis, and for <m>2 \geq x \leq 3</m>.
The graph is undefined at <m>x = 1</m>.
The graph of a piecewise-defined function is shown, for <m>x</m> from <m>0</m> to <m>3</m>.
For <m>0 \leq x \lt 1</m>
the graph looks like a parabola opening downward.
This part of the graph approaches, but does not reach, the point <m>(1,1)</m>.
There is a hollow dot at <m>(1,1)</m>, indicating that <m>f(1)</m> is undefined.
For <m>1 \lt x \leq 2</m> the graph
is a horizontal line segment, with <m>y=1</m>.
For <m>2 \leq x \leq 3</m> the graph again has the appearance of a downward-facing parabola
that begins at <m>(2,1)</m> and ends at <m>(3,1)</m>.
</p>
</description>
<shortdescription>
Example of a discontinuous graph, where the discontinuity is represented by a hollow dot.
Graph of a function with a discontinuity when x=1. Although the limit at 1 exists, f(1) is undefined.
</shortdescription>
<latex-image label="img_continuous1">
\begin{tikzpicture}[declare function = {func(\x) = (\x &gt;= 0)*(\x &lt;= 1)*(-(\x-1/4)^2+1/16+1.5) + (\x &gt; 1)*(\x &lt;= 2) + (\x &gt; 2)*(\x &lt;= 3)*((2-\x)*(\x-3)+1);}]
Expand Down Expand Up @@ -202,12 +207,12 @@
<image width="47%">
<description>
<p>
Shows a graph with domain <m>-2</m> to <m>3</m>. There are five
straight lines, each parallel with the <m>x</m> axis. Each of the lines is
one unit in length and undefined on its right side, but defined on
their left. Line one is defined by the points <m>(-2, -2), (-1, -2)</m>,
line two <m>(-1, -1), (0, -1)</m>, line <m>3</m> <m>(0, 0), (1, 0)</m>, line <m>4</m>
<m>(1, 1), (2, 1)</m>, and line <m>5</m> <m>(2, 2), (3, 2)</m>.
Shows the graph of the greatest integer function, for <m>x</m> from <m>-2</m> to <m>3</m>. There are five
horizontal line segments in a <q>staircase</q> configuration, ascending from left to right. Each segment is
one unit in length and includes its left endpoint, but the right endpoint of each segment is not included.
The first segment is from <m>(-2, -2)</m> to <m>(-1, -2)</m>,
the second from <m>(-1, -1)</m> to <m>(0, -1)</m>, the third from <m>(0, 0)</m> to <m>(1, 0)</m>,
the fourth from <m>(1, 1)</m> to <m>(2, 1)</m>, and the fifth from <m>(2, 2)</m> to <m>(3, 2)</m>.
</p>
</description>
<shortdescription>
Expand Down Expand Up @@ -881,17 +886,16 @@
<image>
<description>
<p>
Shows the graph of a function on the domain <m>0</m> to <m>4</m>.
The graph is has a downward curve
and for <m>x = 2</m> the function is defined by the point <m>(2, 1)</m>.
The point <m>(2, 1)</m> shows a removable discontinuity because the graph
is undefined at <m>x = 2</m>, but the point shows that the function is defined
at <m>x = 2</m>.
A portion of the graph of a function is shown, for <m>x</m> from <m>0</m> to <m>4</m>.
The graph has the shape of a parabola opening downward,
but at <m>x=2</m> there is a hole in the graph,
and instead the point <m>(2,1)</m> (which is not on the graph) is plotted.
The graph of this function illustrates a removable discontinuity because
<m>\lim_{x\to 2}f(x)</m> exists, but does not equal <m>f(2)</m>.
</p>
</description>
<shortdescription>
Graph showing a removable discontinuity by having the point (2, 1)
where f(2) is undefined without the point.
Graph showing a removable discontinuity: a hole in the graph when x=2 shows that the limit and function values disagree.
</shortdescription>
<latex-image label="img_discontinuity_rem">
\begin{tikzpicture}
Expand All @@ -917,14 +921,21 @@
<image>
<description>
<p>
Shows the graph of a function on the domain <m>0</m> to <m>4</m>.
When approching <m>x = 2</m> from the left hand side <m>f(x)</m> is
undefined, but when coming from the right hand side <m>f(x) = 1</m>. For the
interval <m>0 \lt x \leq 2</m> the graph is curved downward and for the
The graph of a function is shown for <m>x</m> from <m>0</m> to <m>4</m>.
As <m>x</m> approaches <m>2</m> from the left,
the graph of <m>f</m> approaches a point that is not part of the graph,
as indicated by a hollow dot.
As <m>x</m> approaches <m>2</m> from the right,
the graph of <m>f</m> approaches a point that is part of the graph,
as indicated by a solid dot.
The point marked by the solid dot lies below the point marked by the hollow dot,
illustrating that the left and right hand limits are different as <m>x\to 2</m>.
</p>

<p>
On the interval <m>0 \lt x \leq 2</m> the graph is curved downward and on the
interval <m>2 \leq x \leq 4</m> the graph is a straight line with a
positive slope. Because <m>f(x)</m> is undefined at <m>x = 2</m>
when coming from the left, but is defined coming from the right,
there is a jump discontinuity.
positive slope.
</p>
</description>
<shortdescription>
Expand Down Expand Up @@ -954,15 +965,12 @@
<image>
<description>
<p>
Shows the graph of a function on the domain <m>0</m> to <m>4</m>.
The graph of a function is shown for <m>x</m> from <m>0</m> to <m>4</m>.
There is a
vertical dotted line at <m>x = 2</m> illustrating an asymptote.
As <m>x</m> approaches <m>2</m> from both sides the value of <m>f(x)</m>
approaches infinity. The graph also has an asymptote at <m>y = 0</m>.
On both sides of the dotted vertical line the graph has an upward
curve with an increasing slope at <m>x</m> gets closer to <m>2</m>.
The asymptote at <m>x = 2</m> causes there to be an infinite
discontinuity.
vertical dotted line at <m>x = 2</m> illustrating a vertical asymptote.
As <m>x</m> approaches <m>2</m> from either side,
the graph of <m>f</m> extends upward along the asymptote,
indicating that the value of <m>f(x)</m> is increasing without bound.
</p>
</description>
<shortdescription>
Expand Down
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