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Merged
merged 12 commits into from
Dec 24, 2024
Merged

Sage images for CO, SQ, and PS #529

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23b8c84
add sage images for CO4
cg2wilson Dec 20, 2024
60d7c0a
LF6 update (#368)
AbbyANoble Dec 20, 2024
1cfa2e3
Add sage images for AD (#439)
cg2wilson Dec 20, 2024
cf52edc
IN Sage Images (#442)
cg2wilson Dec 20, 2024
f14c522
add sage images for CO4
cg2wilson Dec 20, 2024
27f3955
Merge branch 'cg2wilson-CO-SQ-PS-sageimgs' of https://github.com/Team…
siwelwerd Dec 20, 2024
79deaa2
Use f string
siwelwerd Dec 20, 2024
047435e
Update source/calculus/source/07-CO/04.ptx
cg2wilson Dec 20, 2024
9f3f5b6
add CO6 sage images
cg2wilson Dec 23, 2024
4a79411
fixed CO6 sage image
cg2wilson Dec 24, 2024
ff27398
added sage images for SQ6
cg2wilson Dec 24, 2024
20261c0
added sage image for PS1
cg2wilson Dec 24, 2024
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47 changes: 10 additions & 37 deletions source/calculus/source/03-AD/02.ptx
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Original file line number Diff line number Diff line change
Expand Up @@ -51,43 +51,16 @@ Notice that this is obtained by writing the tangent line to <m>f(x)</m> at <m>(a
<task><p>Sketch the tangent line <m>L(x)</m> on the same plane as the graph of <m>\ln(x)</m>. What do you notice?
</p>
<figure>
<image width="50%" xml:id="graph-tangent-line-plane-ln">
<latex-image>
\begin{minipage}{\textwidth}
\begin{center}
\begin{tikzpicture}[scale=0.9]
\begin{axis}[
axis lines=middle,
grid=major,
xmin=0, xmax=5,
ymin=-2, ymax=2,
% xtick={0,10,...,80},
% ytick={0,10,...,50},
% yticklabels={0, 0.01, 0.02, 0.03, 0.04, 0.05},
tick style={thick},
% x label style={at={(axis description cs:1,0.7)}},
% y label style={at={(axis description cs:0.4,1)}},
ylabel=$y$,
xlabel=$x$,
]
\addplot[domain=0.1:5, blue, ultra thick] {ln(x)} node [pos=0.8,above left , ultra thick] {$\boldsymbol{\ln(x)}$};
% \addplot [only marks, blue] table {
% 40 20
% };
% \addplot[only marks, color=blue, nodes near coords={$(40,20)$}] coordinates {(30,20)};
% \addplot[domain=20:70, black, thick] {(x-40)+20} node [pos=0.6, below right, ultra thick] {$\boldsymbol{L(x)}$};
% \addplot [only marks, black] table {
% 20 0
% };
% \addplot[only marks, color=black, nodes near coords={$(20,0)$}] coordinates {(30,0)};
\end{axis}
\end{tikzpicture}
\end{center}
\end{minipage}
</latex-image>
</image>
<caption>The graph of <m> \ln(x)</m></caption>
</figure>
<image width="50%" xml:id="graph-tangent-line-plane-ln">
<sageplot>
x = var('x')
f = ln(x)
p = plot(f,(x,0.1,5), gridlines=True, axes_labels=('$x$','$y$'), thickness=2, aspect_ratio = 1.25)
p
</sageplot>
</image>
<caption>The graph of <m> \ln(x)</m></caption>
</figure>
</task>
</activity>

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87 changes: 56 additions & 31 deletions source/calculus/source/03-AD/04.ptx
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Expand Up @@ -26,30 +26,15 @@
</p>

<figure xml:id="height-function">
<image width="50%" xml:id="graph-parabolic-height-function">
<latex-image>
\begin{tikzpicture}[scale=1]
\begin{axis}[
samples = 900,
axis lines=middle,
grid=major,
% xmin=0, xmax=4,
ymin=0, ymax=70,
% xtick={0,0.5,...,4},
% ytick={-2,-1,...,10},
% tick style={thick},
% x label style={at={(axis description cs:1,0.7)}},
% y label style={at={(axis description cs:0.4,1)}},
ylabel=$s(t)$,
xlabel=$t$,
]
\addplot[domain=0:3, blue, thick] {-16*x^2+32*x+48};
\end{axis}
\end{tikzpicture}

</latex-image>
</image>
<caption>The graph of <m>s(t) = -16t^2 + 32t + 48</m></caption>
<image width="50%" xml:id="graph-parabolic-height-function">
<sageplot>
x = var('x')
f = -16*x^2+32*x+48
p = plot(f,(x,0,3), gridlines=True, axes_labels=('$t$','$s(t)$'), thickness=2, aspect_ratio = .05)
p
</sageplot>
</image>
<caption>The graph of <m>s(t) = -16t^2 + 32t + 48</m></caption>
</figure>
</example>

Expand Down Expand Up @@ -101,22 +86,62 @@
<p>For each of the following figures, decide where the global extrema are located.</p>
</introduction>
<task>
<figure xml:id="figure-evt-int">
<image width="25%" source="evt_int.png" />
<!-- <caption>A.</caption> -->
<figure xml:id="figure-evt-int">
<image width="25%">
<sageplot>
x = var('x')
f = sin(x)
ticks = [[-pi/2, 0, pi/2, pi, 3*pi/2, 2*pi, 5*pi/2],[-1.5,-1,-0.5,0,0.5,1,1.5]]
p = plot(f,(x,0,2*pi), xmin = -pi/2, xmax = 5*pi/2, ymin = -1.5, ymax=1.5, ticks=ticks, tick_formatter=[pi,None], thickness=2, gridlines=True, aspect_ratio=1.5)
c1 = circle((0,0),0.05,fill=True)
c2 = circle((2*pi,0),0.05,fill=True)
p+c1+c2
</sageplot>
</image>
<!-- <caption>A.</caption> -->
</figure>
</task>
</task>
<task><figure xml:id="figure-evt-endpoints">
<image width="25%" source="evt_endpts.png" />
<image width="25%">
<sageplot>
x=var('x')
f(x) = exp(-x) + 1
p = plot(f,(x,0,3), ymin = -1, ymax = 3, gridlines=True, thickness=2, aspect_ratio=1)
q = plot(4,(x,-1,4), ymin=-1, ymax=3, gridlines=True, thickness=2, aspect_ratio=1)
c1 = circle((0,f(0)), 0.05, fill=True)
c2 = circle((3,f(3)),0.05, fill=True)
p+c1+c2+q
</sageplot>
</image>
<!-- <caption>B.</caption> -->
</figure></task>
<task><figure xml:id="figure-evt-mixed">
<image width="25%" source="evt_mixed.png" />
<image width="25%">
<sageplot>
x=var('x')
f(x) = -x^3+2*x^2
c1 = circle((-0.5,f(-0.5)),0.05,fill=True)
c2 = circle((2.2,f(2.2)),0.05,fill=True)
p = plot(f,(x,-0.5,2.2),ymin=-2,ymax=2,thickness=2,gridlines=True,aspect_ratio=1)
q = plot(3,(x,-1,3),ymin=-2,ymax=2,aspect_ratio=1)
c1+c2+p+q
</sageplot>
</image>
<!-- <caption>C.</caption> -->
</figure></task>
<task>
<figure xml:id="figure-evt-mixed2">
<image width="25%" source="evt_mixed2.png" />
<image width="25%">
<sageplot>
x=var('x')
f(x) = abs(-(x-1)^(1/3))
c1 = circle((0,f(0)),0.05,fill=True)
c2 = circle((3,f(3)),0.05,fill=True)
p = plot(f,(x,0,3),ymin=-1,ymax=2,thickness=2,gridlines=True,aspect_ratio=1)
q = plot(3,(x,-1,3.5),ymin=-1,ymax=2,aspect_ratio=1)
c1+c2+p+q
</sageplot>
</image>
<!-- <caption>D.</caption> -->
</figure>
</task>
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113 changes: 106 additions & 7 deletions source/calculus/source/03-AD/06.ptx
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Expand Up @@ -28,7 +28,36 @@

<figure xml:id="concavity-1">
<caption>Three increasing functions</caption>
<image width="100%" source="concavity-1" />
<sidebyside widths = "30% 30% 30%">
<image xml:id="concavity-1-down">
<sageplot>
x = var('x')
f = 2*exp(4*x-3)
ticks=[[],[]]
p = plot(f,(x,.2,1), xmin = -10, xmax = 1, ymin = -1, ymax = 3, gridlines=True,thickness=2, ticks=ticks, aspect_ratio=.2)
p
</sageplot>
</image>
<image xml:id="concavity-1-none">
<sageplot>
x = var('x')
f = x+.75
ticks=[[],[]]
p = plot(f,(x,.05,1), xmin = -10, xmax = 1, ymin = -1, ymax = 3, gridlines=True,thickness=2, ticks=ticks, aspect_ratio=.25)
p
</sageplot>
</image>
<image xml:id="concavity-1-up">
<sageplot>
x = var('x')
f = (x-1.5)^3+2.5
ticks=[[],[]]
p = plot(f,(x,.25,1.25), ymin = -1, ymax = 3, gridlines=True,thickness=2, ticks=ticks, aspect_ratio=.25)
p
</sageplot>
</image>
</sidebyside>

</figure>
</introduction>
<task>
Expand Down Expand Up @@ -91,7 +120,35 @@
</p>
<figure xml:id="concavity-2" permid="PJf">
<caption>From left to right, three functions that are all decreasing.</caption>
<image width="100%" source="concavity-2" />
<sidebyside widths="30% 30% 30%">
<image xml:id="concavity-2-up">
<sageplot>
x = var('x')
f = -(x-1.5)^3+.5
ticks=[[],[]]
p = plot(f,(x,.25,1.25), ymin = -1, ymax = 3, gridlines=True,thickness=2, ticks=ticks, aspect_ratio=.25)
p
</sageplot>
</image>
<image xml:id="concavity-2-none">
<sageplot>
x = var('x')
f = -2*x + 3
ticks = [[],[]]
p = plot(f, (x,.25, 1.25), ymin = -1, ymax = 3, gridlines=True, thickness=2, ticks=ticks, aspect_ratio = 0.25)
p
</sageplot>
</image>
<image xml:id="concavity-2-down">
<sageplot>
x = var('x')
f = -(x)^3+2.5
ticks=[[],[]]
p = plot(f,(x,.25,1.25), ymin = -1, ymax = 3, gridlines=True,thickness=2, ticks=ticks, aspect_ratio=.25)
p
</sageplot>
</image>
</sidebyside>
</figure>

</introduction>
Expand Down Expand Up @@ -148,12 +205,54 @@
<activity xml:id="activity-derivative-concavity3a">
<statement><p>Look at in <xref ref="concavity-3"/>. Which curve is concave up? Which one is concave down? Why? Try to explain using the graph!</p>

<figure xml:id="concavity-3" permid="vQo">
<caption>Two concavity, which is which? </caption>
<image width="90%" source="concavity-3" />
</figure>
<figure xml:id="concavity-3" permid="vQo">
<caption>Two concavities, which is which? </caption>
<sidebyside widths="45% 45%">
<image>
<sageplot>
x = var('x')
f(x) = (x-1)^2 + 1
line1 = -3*(x+0.5)+f(-0.5)
line2 = -1*(x-0.5)+f(0.5)
line3 = (x-1.5)+f(1.5)
line4 = 3*(x-2.5)+f(2.5)
p1 = plot(f,(x,-1,3), ymin = 0, ymax = 6, gridlines=True,thickness=2, aspect_ratio=1)
p2 = plot(line1,(x,-.75,-.25), color="green", thickness=2.5)
p3 = plot(line2,(x,.25,.75), color="green", thickness=2.5)
p4 = plot(line3,(x,1.25,1.75), color="green", thickness=2.5)
p5 = plot(line4,(x,2.25,2.75), color="green", thickness=2.5)
c1 = circle((-.5,f(-.5)),0.1,fill=True,facecolor="red", aspect_ratio="automatic")
c2 = circle((.5,f(.5)),0.1,fill=True,facecolor="red", aspect_ratio="automatic")
c3 = circle((1.5,f(1.5)),0.1,fill=True,facecolor="red", aspect_ratio="automatic")
c4 = circle((2.5,f(2.5)),0.1,fill=True,facecolor="red", aspect_ratio="automatic")
p1+p2+p3+p4+p5+c1+c2+c3+c4
</sageplot>
</image>
<image>
<sageplot>
x = var('x')
f(x) = -(x-1)^2 +2
line1 = 3*(x+0.5)+f(-0.5)
line2 = 1*(x-0.5)+f(0.5)
line3 = -(x-1.5)+f(1.5)
line4 = -3*(x-2.5)+f(2.5)
p1 = plot(f,(x,-1,3), ymin = -3, ymax = 3, gridlines=True,thickness=2, aspect_ratio=1)
p2 = plot(line1,(x,-.75,-.25), color="green", thickness=2.5)
p3 = plot(line2,(x,.25,.75), color="green", thickness=2.5)
p4 = plot(line3,(x,1.25,1.75), color="green", thickness=2.5)
p5 = plot(line4,(x,2.25,2.75), color="green", thickness=2.5)
c1 = circle((-.5,f(-.5)),0.1,fill=True,facecolor="red", aspect_ratio="automatic")
c2 = circle((.5,f(.5)),0.1,fill=True,facecolor="red", aspect_ratio="automatic")
c3 = circle((1.5,f(1.5)),0.1,fill=True,facecolor="red", aspect_ratio="automatic")
c4 = circle((2.5,f(2.5)),0.1,fill=True,facecolor="red", aspect_ratio="automatic")
p1+p2+p3+p4+p5+c1+c2+c3+c4
</sageplot>
</image>
</sidebyside>

</figure>

</statement></activity>
</statement></activity>

<definition xml:id="concavity-and-first-derivative" permid="hcP">
<statement>
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24 changes: 20 additions & 4 deletions source/calculus/source/03-AD/07.ptx
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Expand Up @@ -21,10 +21,18 @@
Which of the following features best describe the curve graphed below? </p>


<figure xml:id="dec-cdown">
<figure xml:id="dec-cdown">
<!-- <caption>A curve</caption> -->
<image width="30%" source="dec-cdown.png" />
</figure>
<image width="30%">
<sageplot>
x = var('x')
f = -(x)^3+2.5
ticks=[[],[]]
p = plot(f,(x,.25,1.25), ymin = -1, ymax = 3, gridlines=True,thickness=2, ticks=ticks, aspect_ratio=.25)
p
</sageplot>
</image>
</figure>
</introduction>


Expand All @@ -47,7 +55,15 @@

<figure xml:id="inc-cdown">
<!-- <caption>A curve</caption> -->
<image width="30%" source="inc-cdown.png" />
<image width="30%">
<sageplot>
x = var('x')
f = (x-1.5)^3+2.5
ticks=[[],[]]
p = plot(f,(x,.25,1.25), ymin = -1, ymax = 3, gridlines=True,thickness=2, ticks=ticks, aspect_ratio=.25)
p
</sageplot>
</image>
</figure>


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