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Merged
jford1906 merged 6 commits into from
Dec 20, 2024
Merged

IN Sage Images #442

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a6a5af9
add IN1 sage images
cg2wilson Dec 5, 2024
6d6be6b
add sage images for IN2
cg2wilson Dec 6, 2024
0173f08
add IN5 sage images
cg2wilson Dec 6, 2024
41fa552
add IN8 sage images
cg2wilson Dec 8, 2024
5d403e4
Update with main (#472)
StevenClontz Dec 17, 2024
f23a339
Merge pull request #474 from TeamBasedInquiryLearning/main
StevenClontz Dec 17, 2024
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26 changes: 23 additions & 3 deletions source/calculus/source/04-IN/01.ptx
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Original file line number Diff line number Diff line change
Expand Up @@ -109,9 +109,29 @@
<activity>
<introduction> <p>
The graph of <m>g(t)</m> and the areas <m>A_1, A_2, A_3</m> are given below. </p>
<figure xml:id="figure-signed-areas">
<image width="100%" source="fig2d.JPG" />
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@siwelwerd siwelwerd Dec 9, 2024

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Does this mean we can also delete the fig2d.JPG file? Note that it will still be archived on Github so it's not permanently deleted.

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@cg2wilson cg2wilson Dec 9, 2024

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i think so? i was going to wait to delete the .jpg and .png files until the pull requests were final for each module.

</figure>
<figure xml:id="figure-signed-areas">
<sidebyside widths="50% 50%">
<image>
<sageplot>
x = var('x')
f = -0.0019378058*x^5+0.0272617825*x^4-0.0281391103*x^3-0.6767556453*x^2 + 1.6980068882*x-0.0048902147
p = plot(f,(x,0,10),thickness=2, gridlines=True, aspect_ratio=1.5, axes_labels=('$t$','$g(t)$'))
p
</sageplot>
</image>
<image>
<sageplot>
x = var('x')
f = -0.0019378058*x^5+0.0272617825*x^4-0.0281391103*x^3-0.6767556453*x^2 + 1.6980068882*x-0.0048902147
p = plot(f,(x,0,10),thickness=2, gridlines=True, aspect_ratio=1.5, fill=True, axes_labels=('$t$','$g(t)$'))
a1 = text("$A_1 = 2$",(1.25,0.5), fontsize=12, color='black')
a2 = text("$A_2 = 2.5$", (4.75, -0.5), fontsize=12, color='black')
a3 = text("$A_3 = 9$", (8.25,1.75), fontsize=12, color='black')
p+a1+a2+a3
</sageplot>
</image>
</sidebyside>
</figure>
</introduction>
<task> <p> Find <m>\int_{3}^{3} g(t) \, dt</m></p></task>
<task> <p> Find <m>\int_{3}^{6} g(t) \, dt</m></p></task>
Expand Down
175 changes: 107 additions & 68 deletions source/calculus/source/04-IN/02.ptx
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Original file line number Diff line number Diff line change
Expand Up @@ -31,6 +31,26 @@
axes for plotting <m>y = v(t)</m>;
at right, for plotting
<m>y = s(t)</m>.</caption>
<sidebyside widths="50% 50%">
<image>
<sageplot>
x = var('x')
f = 0
ticks = [True,[a for a in (1..8)]]
p = plot(f,(x,0,2.25), thickness=0, ymin = 0.25, ymax = 8.25, gridlines='minor', axes_labels=('hrs','mph'), axes_labels_size=1, aspect_ratio=.25, ticks=ticks)
p
</sageplot>
</image>
<image>
<sageplot>
x = var('x')
f = 0
ticks = [True,[a for a in (1..8)]]
p = plot(f,(x,0,2.25), thickness=0, ymin = 0.25, ymax = 8.25, gridlines='minor', axes_labels=('hrs','miles'), axes_labels_size=1, aspect_ratio=.25, ticks=ticks)
p
</sageplot>
</image>
</sidebyside>
<image width="100%" source="4_1_PA1" />
</figure>

Expand Down Expand Up @@ -130,7 +150,27 @@

<figure xml:id="F-4-1-Act1" permid="qNs">
<caption>The graph of <m>y = v(t)</m>.</caption>
<image source="4_1_Act1" />
<image>
<sageplot>
x = var('x')
f = (x-1)^3 + 2.5
p = plot(f, (x,-.25,2.25), thickness=2, ymin=0, ymax = 3.5, gridlines=True, axes_labels=('hrs','mph'), axes_labels_size=1, aspect_ratio=.6)
a = text("$y = v(t)$",(1, 2.65), fontsize=12, color='black')
p + a
</sageplot>
</image>
<!--
<image>
<sageplot>
x = var('x')
f = (x-1)^3 + 2.5
ticks = [[a for a in (.25,.5..3.5)],[a for a in (.25,.5..3.5)]]
p = plot(f, (x,-.25,2.25), thickness=2, ymin=0, ymax = 3.5, gridlines=True, axes_labels=('hrs','mph'), axes_labels_size=1, aspect_ratio=.6, ticks=ticks)
a = text("$y = v(t)$",(1, 2.65), fontsize=12, color='black')
p + a
</sageplot>
</image>
-->
</figure>
</sidebyside>
</introduction>
Expand Down Expand Up @@ -214,51 +254,64 @@
<figure xml:id="fig-riemann-sum-generic">
<caption>A generic Riemann sum.</caption>
<image width="100%">
<latex-image>
\begin{tikzpicture}
\draw[thick] (0,0) -- (5,0);
\draw[fill=gray!50] (0, 0) rectangle (0.8, 1);
\draw[fill=gray!50] (0.8, 0) rectangle (1.9, 1.75);
\draw[fill=gray!50] (1.9, 0) rectangle (3.4, -1.2);
\draw[fill=gray!50] (3.4, 0) rectangle (4.2, 0.85);
\draw[fill=gray!50] (4.2, 0) rectangle (5.7, 0.35);
\draw[fill=gray!50] (5.7, 0) rectangle (6, -0.5);
\draw[fill=black] (0.2, 1.0) circle (0.05);
\draw[fill=black] (1.55, 1.75) circle (0.05);
\draw[fill=black] (2.15, -1.2) circle (0.05);
\draw[fill=black] (3.8, 0.85) circle (0.05);
\draw[fill=black] (4.5, 0.35) circle (0.05);
\draw[fill=black] (6.0, -0.5) circle (0.05);
\node[above, font=\tiny] at (0.2, 1.0) {$(s_1, f(s_1))$};
\node[above, font=\tiny] at (1.55, 1.75) {$(s_2, f(s_2))$};
\node[below, font=\tiny] at (2.15, -1.2) {$(s_3, f(s_3))$};
\node[above, font=\tiny] at (3.8, 0.85) {$(s_4, f(s_4))$};
\node[above, font=\tiny] at (4.5, 0.35) {$(s_5, f(s_5))$};
\node[below, font=\tiny] at (6.0, -0.5) {$(s_6, f(s_6))$};
\draw[thick, style=dashed, color=blue]
(0, 0.8) .. controls (0.1, 0.9) and (0.1, 1.1) ..
(0.2, 1.0) .. controls (1, 2) and (1, -1.0) ..
(1.55, 1.75) .. controls (1.8, -0.42) and (2.1, 1.9) ..
(2.15, -1.2) .. controls (2.6, -1.3) and (3.2, -1.1) ..
(3.8, 0.85) .. controls (3.9, 0.9) and (3.9, 0.8) ..
(4.5, 0.35) .. controls (4.6, 0.4) and (4.6, 0.3) ..
(6.0, -0.5)
;
\node[font=\tiny] at (0,-0.15) {$x_0$};
\node[font=\tiny] at (0.8,-0.15) {$x_1$};
\node[font=\tiny] at (1.9,-0.15) {$x_2$};
\node[font=\tiny] at (3.4,-0.15) {$x_3$};
\node[font=\tiny] at (4.2,-0.15) {$x_4$};
\node[font=\tiny] at (5.7,-0.15) {$x_5$};
\node[font=\tiny] at (6,-0.15) {$x_6$};
\end{tikzpicture}

%(2.15, -1.2)
%(3.8, 0.85)
%(4.5, 0.35)
%(6.0, -0.5)

</latex-image>
<sageplot>
# Import necessary library
from sage.plot.graphics import Graphics

# Create a new graphics object
geometry = Graphics()

# Add rectangles
rectangles = [
((0, 0), (0.8, 1)),
((0.8, 0), (1.9, 1.75)),
((1.9, 0), (3.4, -1.2)),
((3.4, 0), (4.2, 0.85)),
((4.2, 0), (5.7, 0.35)),
((5.7, 0), (6, -0.5)),
]
for rect in rectangles:
geometry += polygon2d(
[rect[0], (rect[1][0], rect[0][1]), rect[1], (rect[0][0], rect[1][1])],
fill=True, color='lightgray', edgecolor='black'
)

# Add points and their labels
points = [
(0.2, 1.0, "$(s_1, f(s_1))$", "above"),
(1.55, 1.75, "$(s_2, f(s_2))$", "above"),
(2.15, -1.2, "$(s_3, f(s_3))$", "below"),
(3.8, 0.85, "$(s_4, f(s_4))$", "above"),
(4.5, 0.35, "$(s_5, f(s_5))$", "above"),
(6.0, -0.5, "$(s_6, f(s_6))$", "below"),
]
for (x, y, label, position) in points:
geometry += point((x, y), color="black", size=20)
geometry += text(label, (x, y + (0.2 if position == "above" else -0.2)), fontsize=12, color="black")

# Add x-axis labels
x_labels = [
(0, "$x_0$"), (0.8, "$x_1$"), (1.9, "$x_2$"), (3.4, "$x_3$"),
(4.2, "$x_4$"), (5.7, "$x_5$"), (6, "$x_6$")
]
for (x, label) in x_labels:
geometry += text(label, (x, -0.15), fontsize=12, color="black")

# Define the Bézier path
bezier_segments = [
bezier_path([[(0, 0.8), (0.1, 0.9), (0.1, 1.1), (0.2, 1.0)]], alpha=0.75, color = 'blue', thickness=2, linestyle='dashed'),
bezier_path([[(0.2, 1.0), (1, 2), (1, -1.0), (1.55, 1.75)]], alpha=0.75, color = 'blue', thickness=2, linestyle='dashed'),
bezier_path([[(1.55, 1.75), (1.8, -0.42), (2.1, 1.9), (2.15, -1.2)]], alpha=0.75, color = 'blue', thickness=2, linestyle='dashed'),
bezier_path([[(2.15, -1.2), (2.6, -1.3), (3.2, -1.1), (3.8, 0.85)]], alpha=0.75, color = 'blue', thickness=2, linestyle='dashed'),
bezier_path([[(3.8, 0.85), (3.9, 0.9), (3.9, 0.8), (4.5, 0.35)]], alpha=0.75, color = 'blue', thickness=2, linestyle='dashed'),
bezier_path([[(4.5, 0.35), (4.6, 0.4), (4.6, 0.3), (6.0, -0.5)]], alpha=0.75, color = 'blue', thickness=2, linestyle='dashed')
]

# Add the Bézier curves to the graphics
geometry += sum(bezier_segments, Graphics())
geometry.axes(False)
geometry
</sageplot>
</image>
</figure>

Expand Down Expand Up @@ -374,36 +427,22 @@
<p>
Explain how to approximate the area under the curve
<me>
f(x) = -\frac{1}{5} (x-4)(x-10)(x-12)
f(x) = \frac{1}{5} (x-4)(x-10)(x-12)
</me> on the
interval <m>[4,10]</m> using a right Riemann
sum with 3 subintervals.
</p>
<image>
<description>The graph of the function <m>f(x) = -1/5 (x-4)(x-10)(x-12)</m>
<description>The graph of the function <m>f(x) = 1/5 (x-4)(x-10)(x-12)</m>
crosses the <m>x</m>-axis upward at <m>(4,0)</m> and downward at <m>(10,0)</m>
with a maximum at about <m>(6.3, 9.7)</m>.
</description>
<latex-image>
\begin{tikzpicture}
\begin{axis}[
axis lines=middle,
grid=both,
xmin=3,
xmax=11,
ymin=-1,
ymax=12,
xlabel=$x$,
ylabel=$y$,
xtick={3,4,...,10},
ytick={0,1,...,12},
legend pos=north east,
]
\addplot[domain=3:11, smooth, thick, blue] {1/5*(x-4)*(x-10)*(x-12)};
\addlegendentry{{\tiny $f(x)=\frac{1}{5}(x-4)(x-10)(x-12)$}}
\end{axis}
\end{tikzpicture}
</latex-image>
<sageplot>
x = var('x')
f = 0.2*(x-4)*(x-10)*(x-12)
p = plot(f,(x,3,10.5),gridlines=True,ymin = -1, ymax = 11, thickness=2, axes_labels=('$x$','$y$'))
p
</sageplot>
</image>
</statement>
<solution>
Expand Down
85 changes: 77 additions & 8 deletions source/calculus/source/04-IN/05.ptx
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Original file line number Diff line number Diff line change
Expand Up @@ -18,7 +18,15 @@
</introduction>

<figure xml:id="in5-figure-1">
<image width="50%" source="area1.png" />
<image width="50%">
<sageplot>
x= var('x')
f = 0.5*x+2
ticks = [[-4,-3,-2,-1,0,1,2,3,4,5,6,7,8],[1,2,3,4,5,6]]
p = plot(f,(x,-4,8),gridlines=True, thickness=2, axes_labels=('$x$','$f(x)$'), aspect_ratio=1.25, ticks=ticks)
p
</sageplot>
</image>
</figure>
</activity>

Expand All @@ -27,7 +35,14 @@
<p>Approximate the area under the curve <m>f(x)=(x-1)^2+2</m> on the interval <m>[1,5]</m> using a <b>left</b> Riemann sum with four uniform subdivisions. Draw your rectangles on the graph.</p>
</introduction>
<figure xml:id="in5-figure-2">
<image width="50%" source="riemann1.png" />
<image width="50%">
<sageplot>
x = var('x')
f = (x-1)^2 + 2
p = plot(f,(x,0,5), gridlines=True, thickness=2, axes_labels=('$x$','$f(x)$'), aspect_ratio = .25)
p
</sageplot>
</image>
</figure>
</activity>

Expand Down Expand Up @@ -96,21 +111,44 @@
<task>
<p> <m> \displaystyle \int_0^2 \left(x^2+3\right) \, dx </m></p>
<figure xml:id="in5-figure-3">
<image width="50%" source="x2plus3.png" />
<image width="50%">
<sageplot>
x = var('x')
f = x^2 + 3
ticks = [True, [1..12]]
p = plot(f,(x,-3,3), ymin = 0, gridlines=True, thickness=2, axes_labels=('$x$','$y$'),ticks=ticks)
p
</sageplot>
</image>
</figure>
</task>

<task>
<p> <m> \displaystyle \int_1^4 \left(\sqrt{x}\right) \, dx </m></p>
<figure xml:id="in5-figure-4">
<image width="50%" source="sqrtx.png" />
<image width="50%">
<sageplot>
x = var('x')
f = sqrt(x)
p = plot(f,(x,0,6), gridlines=True, thickness=2, axes_labels=('$x$','$y$'))
p
</sageplot>
</image>
</figure>
</task>

<task>
<p> <m> \displaystyle \int_{-\pi/4}^{\pi/2} \left(\cos x\right) \, dx </m></p>
<figure xml:id="in5-figure-5">
<image width="50%" source="cosx.png" />
<image width="50%">
<sageplot>
x = var('x')
f = cos(x)
ticks = [[-pi/2, -pi/4,0,pi/4,pi/2,3*pi/4,pi],True]
p = plot(f,(x,-pi/2,pi), gridlines='minor', thickness=2, axes_labels=('$x$','$y$'), tick_formatter=[pi,None], ticks=ticks)
p
</sageplot>
</image>
</figure>
</task>
</activity>
Expand All @@ -124,7 +162,14 @@
</ol>
</p>
<figure xml:id="in5-figure-6">
<image width="50%" source="linedefint.png" />
<image width="50%">
<sageplot>
x = var('x')
f = 2*x-6
p = plot(f,(x,0,8), gridlines=True, thickness=2, axes_labels=('$x$','$f(x)$'))
p
</sageplot>
</image>
</figure>
<p>What do you notice?</p>
</introduction>
Expand All @@ -134,7 +179,14 @@
<introduction>
<p>Find the area bounded by the curves <m>f(x)=e^x-2</m>, the <m>x</m>-axis, <m>x=0</m>, and <m>x=1</m>. </p>
<figure xml:id="in5-figure-7">
<image width="50%" source="exminus2.png" />
<image width="50%">
<sageplot>
x = var('x')
f = exp(x)-2
p = plot(f,(x,-1,1.5), gridlines=True, thickness=2, axes_labels=('$x$','$f(x)$'))
p
</sageplot>
</image>
</figure>
</introduction>
</activity>
Expand All @@ -147,12 +199,29 @@
<p><m>y=\frac{1}{x^2}</m></p>
<figure xml:id="in5-figure-8">
<image width="50%" source="defintarea1.png" />
<image width="50%">
<sageplot>
x = var('x')
f = 1/x^2
p1 = plot(f,(x,.5,3.5), gridlines=True, thickness=2, axes_labels=('$x$','$y$'))
p2 = plot(f,(x,1,3),fill=True)
p1+p2
</sageplot>
</image>
</figure>
</task>
<task>
<p><m>y=3x^2-x^3</m></p>
<figure xml:id="in5-figure-9">
<image width="50%" source="defintarea2.png" />
<image width="50%">
<sageplot>
x=var('x')
f = 3*x^2-x^3
p1 = plot(f,(x,-1,4),ymin = -2, thickness=2,gridlines=True, axes_labels=('$x$','$y$'))
p2 = plot(f,(x,0,2),fill=True)
p1+p2
</sageplot>
</image>
</figure>
</task>
</activity>
Expand Down
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