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Merge remote-tracking branch 'mattboelkins/worksheets' into worksheets
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@mitchkeller
mitchkeller committed Jul 31, 2024
2 parents 4a2fcf2 + b245dc2 commit 661b9d1
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5 changes: 2 additions & 3 deletions source/acs-activity-workbook-58.xml
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Expand Up @@ -49,13 +49,11 @@
<preface permid="qRN">
<p permid="Dgf">
This Activities Workbook for <pubtitle>Active Calculus Single Variable</pubtitle> collects all the Preview Activities and Activities in a way that each starts on a new page.
The Activities Workbook is designed to be used by students who wish to have a complete set of the activities to work through as they read the book in an electronic format and for instructors who wish to have a one activity per page format to make printing for distribution in class easier.
The Activities Workbook provides space for students to write and organize their work as they complete the activities found in the text.
</p>

<p permid="jno">
The design of this workbook is such that each Preview Activity and Activity starts on a right-hand page.
As a result,
most left-hand pages in this workbook are intentionally left blank as a place for student work associated with one of the adjacent activities.
The workbook is offered for purchase in print form in two volumes:
the first for chapters 1<ndash />4 and the second for chapters 5<ndash />8.
</p>
Expand All @@ -66,6 +64,7 @@
<xi:include href="./chap-6-wb.xml" />
<xi:include href="./chap-7-wb.xml" />
<xi:include href="./chap-8-wb.xml" />

<backmatter>
<appendix xml:id="integral-table" permid="Alz">
<title>A Short Table of Integrals</title>
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7 changes: 2 additions & 5 deletions source/activities/act-4-2-3.xml
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Expand Up @@ -118,11 +118,8 @@
<task workspace="3cm" xml:id="act-4-2-3-task-3">
<statement>
<p>
Use appropriate computing technology<fn>
For instance,
consider the <url href="https://gvsu.edu/s/a9" visual="gvsu.edu/s/a9">applet</url>
and change the function and adjust the locations of the blue points that represent the interval endpoints <m>a</m> and <m>b</m>.
</fn> to compute <m>M_{10}</m> and <m>M_{20}</m>.
Use appropriate computing technology such as <url href="https://gvsu.edu/s/a9" visual="gvsu.edu/s/a9">this applet</url>
to compute <m>M_{10}</m> and <m>M_{20}</m>.
What exact value do you think the middle sum eventually approaches as <m>n</m> increases without bound?
What does that number represent in the physical context of the overall problem?
</p>
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8 changes: 4 additions & 4 deletions source/activities/act-5-1-1.xml
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Expand Up @@ -31,7 +31,7 @@
</figure>
<p/>
</introduction>
<task workspace="3cm" xml:id="act-5-1-1-task-0">
<task workspace="2cm" xml:id="act-5-1-1-task-0">
<statement>
<p>
On what interval(s) is <m>F</m> an increasing function?
Expand All @@ -56,7 +56,7 @@
</p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-1-1-task-1">
<task workspace="2cm" xml:id="act-5-1-1-task-1">
<statement>
<p>
On what interval(s) is <m>F</m> concave up? concave down? neither?
Expand Down Expand Up @@ -85,7 +85,7 @@
</p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-1-1-task-2">
<task workspace="2cm" xml:id="act-5-1-1-task-2">
<statement>
<p>
At what point(s) does <m>F</m> have a relative minimum? a relative maximum?
Expand All @@ -110,7 +110,7 @@
</p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-1-1-task-3">
<task workspace="6cm" xml:id="act-5-1-1-task-3">
<statement>
<p>
Use the given information to determine the exact value of <m>F(x)</m> for <m>x = 1, 2, \ldots, 7</m>.
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8 changes: 4 additions & 4 deletions source/activities/act-5-1-2.xml
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Expand Up @@ -14,7 +14,7 @@
<!-- **********************************************************************-->
<worksheet label="ws-act-5-1-2">
<page>
<activity xml:id="act-5-1-2" workspace="3cm">
<activity xml:id="act-5-1-2" workspace="8cm">
<introduction>
<p>
For each of the following functions,
Expand All @@ -27,7 +27,7 @@

</p>
</introduction>
<task workspace="3cm" xml:id="act-5-1-2-task-0">
<task workspace="9cm" xml:id="act-5-1-2-task-0">
<statement>
<p>
original function:
Expand All @@ -49,7 +49,7 @@
</p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-1-2-task-1">
<task workspace="9cm" xml:id="act-5-1-2-task-1">
<statement>
<p>
original function: <m>h(x) = \sin(x)</m>; initial condition:
Expand All @@ -68,7 +68,7 @@
</p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-1-2-task-2">
<task workspace="8cm" xml:id="act-5-1-2-task-2">
<statement>
<p>
original function:
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2 changes: 1 addition & 1 deletion source/activities/act-5-1-3.xml
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Expand Up @@ -115,7 +115,7 @@
</p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-1-3-task-3">
<task workspace="6cm" xml:id="act-5-1-3-task-3">
<statement>
<p>
Use the given information to determine the exact values of <m>A(0)</m>,
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6 changes: 3 additions & 3 deletions source/activities/act-5-2-1.xml
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Expand Up @@ -31,7 +31,7 @@

</p>
</introduction>
<task workspace="3cm" xml:id="act-5-2-1-task-0">
<task workspace="2cm" xml:id="act-5-2-1-task-0">
<statement>
<p>
What does the Second FTC tell us about the relationship between <m>A</m> and <m>f</m>?
Expand All @@ -53,7 +53,7 @@
</p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-2-1-task-1">
<task workspace="4cm" xml:id="act-5-2-1-task-1">
<statement>
<p>
Compute <m>A(1)</m> and <m>A(3)</m> exactly.
Expand All @@ -75,7 +75,7 @@
</p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-2-1-task-2">
<task workspace="6cm" xml:id="act-5-2-1-task-2">
<statement>
<p>
Sketch a precise graph of
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6 changes: 3 additions & 3 deletions source/activities/act-5-2-2.xml
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Expand Up @@ -25,7 +25,7 @@
<image width="100%" source="images/5_2_Act2"/>
</figure>
</introduction>
<task workspace="3cm" xml:id="act-5-2-2-task-0">
<task workspace="1cm" xml:id="act-5-2-2-task-0">
<statement>
<p>
On the axes at left in <xref ref="F-5-2-Act2">Figure</xref>,
Expand Down Expand Up @@ -70,7 +70,7 @@
</p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-2-2-task-2">
<task workspace="5cm" xml:id="act-5-2-2-task-2">
<statement>
<p>
Use the first derivative test to determine the intervals on which <m>F</m> is increasing and decreasing.
Expand Down Expand Up @@ -116,7 +116,7 @@
</p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-2-2-task-4">
<task workspace="6cm" xml:id="act-5-2-2-task-4">
<statement>
<p>
Using technology appropriately,
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14 changes: 7 additions & 7 deletions source/activities/act-5-2-3.xml
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Expand Up @@ -14,15 +14,15 @@
<!-- **********************************************************************-->
<worksheet label="ws-act-5-2-3">
<page>
<activity xml:id="act-5-2-3" workspace="3cm">
<activity xml:id="act-5-2-3" workspace="4cm">
<introduction>
<p>
Evaluate each of the following derivatives and definite integrals.
Clearly cite whether you use the First or Second FTC in so doing.

</p>
</introduction>
<task workspace="3cm" xml:id="act-5-2-3-task-0">
<task workspace="4cm" xml:id="act-5-2-3-task-0">
<statement>
<p>
<m>\frac{d}{dx} \left[ \int_4^x e^{t^2} \, dt \right]</m>
Expand All @@ -43,7 +43,7 @@
</p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-2-3-task-1">
<task workspace="4cm" xml:id="act-5-2-3-task-1">
<statement>
<p>
<m>\int_{-2}^x \frac{d}{dt} \left[ \frac{t^4}{1+t^4} \right] \, dt</m>
Expand All @@ -64,7 +64,7 @@
</p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-2-3-task-2">
<task workspace="4cm" xml:id="act-5-2-3-task-2">
<statement>
<p>
<m>\frac{d}{dx} \left[ \int_{x}^1 \cos(t^3) \, dt \right]</m>
Expand All @@ -85,7 +85,7 @@
</p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-2-3-task-3">
<task workspace="5cm" xml:id="act-5-2-3-task-3">
<statement>
<p>
<m>\int_{3}^x \frac{d}{dt} \left[ \ln(1+t^2) \right] \, dt</m>
Expand All @@ -106,9 +106,9 @@
</p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-2-3-task-4">
<task workspace="4cm" xml:id="act-5-2-3-task-4">
<statement>
<p><m>\frac{d}{dx} \left[ \int_4^{x^3} \sin(t^2) \, dt \right]</m> .
<p><m>\frac{d}{dx} \left[ \int_4^{x^3} \sin(t^2) \, dt \right]</m>
</p>
</statement>
<hint>
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14 changes: 7 additions & 7 deletions source/activities/act-5-3-1.xml
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Expand Up @@ -14,15 +14,15 @@
<!-- **********************************************************************-->
<worksheet label="ws-act-5-3-1">
<page>
<activity xml:id="act-5-3-1" workspace="3cm">
<activity xml:id="act-5-3-1" workspace="6cm">
<introduction>
<p>
Evaluate each of the following indefinite integrals.
Check each antiderivative that you find by differentiating.

</p>
</introduction>
<task workspace="3cm" xml:id="act-5-3-1-task-0">
<task workspace="6cm" xml:id="act-5-3-1-task-0">
<statement>
<p>
<m>\int \sin(8-3x) \, dx</m>
Expand All @@ -44,7 +44,7 @@
</p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-3-1-task-1">
<task workspace="6cm" xml:id="act-5-3-1-task-1">
<statement>
<p>
<m>\int \sec^2 (4x) \, dx</m>
Expand All @@ -66,7 +66,7 @@
</p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-3-1-task-2">
<task workspace="6.5cm" xml:id="act-5-3-1-task-2">
<statement>
<p>
<m>\int \frac{1}{11x - 9} \, dx</m>
Expand All @@ -88,7 +88,7 @@
</p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-3-1-task-3">
<task workspace="6cm" xml:id="act-5-3-1-task-3">
<statement>
<p>
<m>\int \csc(2x+1) \cot(2x+1) \, dx</m>
Expand All @@ -110,7 +110,7 @@
</p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-3-1-task-4">
<task workspace="6cm" xml:id="act-5-3-1-task-4">
<statement>
<p>
<m>\int \frac{1}{\sqrt{1-16x^2}}\, dx</m>
Expand All @@ -133,7 +133,7 @@
we see that <m>\int \frac{1}{\sqrt{1-16x^2}}\, dx = \frac{1}{4} \arcsin(4x) + C</m></p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-3-1-task-5">
<task workspace="6cm" xml:id="act-5-3-1-task-5">
<statement>
<p>
<m>\int 5^{-x}\, dx</m>
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8 changes: 4 additions & 4 deletions source/activities/act-5-3-2.xml
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Expand Up @@ -14,7 +14,7 @@
<!-- **********************************************************************-->
<worksheet label="ws-act-5-3-2">
<page>
<activity xml:id="act-5-3-2" workspace="3cm">
<activity xml:id="act-5-3-2" workspace="7cm">
<introduction>
<p>
Evaluate each of the following indefinite integrals by using these steps:
Expand All @@ -34,7 +34,7 @@
You should come up with the integrand originally given.
</p></li></ul></p>
</introduction>
<task workspace="3cm" xml:id="act-5-3-2-task-0">
<task workspace="7cm" xml:id="act-5-3-2-task-0">
<statement>
<p>
<m>\int \frac{x^2}{5x^3+1} \, dx</m>
Expand All @@ -61,7 +61,7 @@
</p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-3-2-task-1">
<task workspace="8cm" xml:id="act-5-3-2-task-1">
<statement>
<p>
<m>\int e^x \sin(e^x) \, dx</m>
Expand All @@ -86,7 +86,7 @@
</p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-3-2-task-2">
<task workspace="7cm" xml:id="act-5-3-2-task-2">
<statement>
<p>
<m>\int \frac{\cos(\sqrt{x})}{\sqrt{x}} \, dx</m>
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8 changes: 4 additions & 4 deletions source/activities/act-5-3-3.xml
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Expand Up @@ -14,14 +14,14 @@
<!-- **********************************************************************-->
<worksheet label="ws-act-5-3-3">
<page>
<activity xml:id="act-5-3-3" workspace="3cm">
<activity xml:id="act-5-3-3" workspace="7cm">
<introduction>
<p>
Evaluate each of the following definite integrals exactly through an appropriate <m>u</m>-substitution.

</p>
</introduction>
<task workspace="3cm" xml:id="act-5-3-3-task-0">
<task workspace="10cm" xml:id="act-5-3-3-task-0">
<statement>
<p>
<m>\int_1^2 \frac{x}{1 + 4x^2} \, dx</m>
Expand All @@ -46,7 +46,7 @@
</p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-3-3-task-1">
<task workspace="10cm" xml:id="act-5-3-3-task-1">
<statement>
<p>
<m>\int_0^1 e^{-x} (2e^{-x}+3)^{9} \, dx</m>
Expand All @@ -72,7 +72,7 @@
</p>
</solution>
</task>
<task workspace="3cm" xml:id="act-5-3-3-task-2">
<task workspace="10cm" xml:id="act-5-3-3-task-2">
<statement>
<p>
<m>\int_{2/\pi}^{4/\pi} \frac{\cos\left(\frac{1}{x}\right)}{x^{2}} \,dx</m>
Expand Down
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