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Merge pull request #990 from mooculus/Ramsey_Sp24ExercisesUpdate
Ramsey sp24 exercises update
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‎antiderivatives/exercises/additionalList.tex

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\documentclass{xourse}
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\input{../../preamble.tex}
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\begin{document}
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\part{Antiderivatives}
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% \practice{q14429v1.tex}
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% \practice{q14430v1.tex}
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% \practice{q14431v1.tex}
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% \practice{q14432v1.tex}
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% \practice{q14433v1.tex}
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% \practice{q14434v1.tex}
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\practice{q14435v1.tex}
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% \practice{q14513v1.tex}
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% \practice{05_01_ex_07.tex}
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% \practice{05_01_ex_09.tex}
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% \practice{05_01_ex_11.tex}
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% \practice{05_01_ex_13.tex}
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% \practice{05_01_ex_16.tex}
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% \practice{05_01_ex_20.tex}
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% \practice{05_01_ex_24.tex}
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% \practice{05_01_ex_25.tex}
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% \practice{05_01_ex_27.tex}
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% \practice{05_01_ex_29.tex}
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% \practice{05_02_ex_26.tex}
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\practice{05_02_ex_27.tex}
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% \practice{05_02_ex_28.tex}
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% \practice{05_02_ex_29.tex}
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% \practice{antiderivativeTrueFalse8.tex}
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% \practice{diffEqApprox1.tex}
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% \practice{positionFromVelocity1.tex}
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% \practice{velocityFromAcceleration.tex}
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% \practice{positionFromVelocity2.tex}
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% \practice{positionFromVelocity3.tex}
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\end{document}

‎antiderivatives/exercises/exerciseList.tex

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\part{Antiderivatives}
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\practice{q14429v1.tex}
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\practice{q14430v1.tex}
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\practice{q14431v1.tex}
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\practice{q14432v1.tex}
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\practice{q14433v1.tex}
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\practice{q14434v1.tex}
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%\practice{q14435v1.tex}
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\practice{q14513v1.tex}
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\practice{05_01_ex_07.tex}
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\practice{05_01_ex_09.tex}
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\practice{05_01_ex_11.tex}
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\practice{05_01_ex_13.tex}
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\practice{05_01_ex_16.tex}
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\practice{05_01_ex_20.tex}
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\practice{05_01_ex_24.tex}
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\practice{05_01_ex_25.tex}
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\practice{05_01_ex_27.tex}
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\practice{05_01_ex_29.tex}
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\practice{05_02_ex_26.tex}
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\practice{05_02_ex_27.tex}
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\practice{05_02_ex_28.tex}
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\practice{05_02_ex_29.tex}
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\practice{antiderivativeTrueFalse8.tex}
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\practice{diffEqApprox1.tex}
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\practice{positionFromVelocity1.tex}
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\practice{velocityFromAcceleration.tex}
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\practice{positionFromVelocity2.tex}
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\practice{positionFromVelocity3.tex}
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\practice{q14429v1.tex}
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\practice{q14430v1.tex}
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\practice{q14431v1.tex}
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\practice{q14432v1.tex}
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\practice{q14433v1.tex}
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\practice{q14434v1.tex}
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% \practice{q14435v1.tex}
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\practice{q14513v1.tex}
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\practice{05_01_ex_07.tex}
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\practice{05_01_ex_09.tex}
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\practice{05_01_ex_11.tex}
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\practice{05_01_ex_13.tex}
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\practice{05_01_ex_16.tex}
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\practice{05_01_ex_20.tex}
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\practice{05_01_ex_24.tex}
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\practice{05_01_ex_25.tex}
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\practice{05_01_ex_27.tex}
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\practice{05_01_ex_29.tex}
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\practice{05_02_ex_26.tex}
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% \practice{05_02_ex_27.tex}
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\practice{05_02_ex_28.tex}
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\practice{05_02_ex_29.tex}
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\practice{antiderivativeTrueFalse8.tex}
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\practice{diffEqApprox1.tex}
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\practice{positionFromVelocity1.tex}
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\practice{velocityFromAcceleration.tex}
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\practice{positionFromVelocity2.tex}
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\practice{positionFromVelocity3.tex}
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\end{document}

‎antiderivatives/exercises/q14432v1.tex

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\documentclass{ximera}
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\input{../../preamble.tex}
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\author{Emma Smith Zbarsky\and Nela Lakos}
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\author{Emma Smith Zbarsky\and Nela Lakos \and Bobby Ramsey}
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\license{Creative Commons Attribution 3.0 Unported}
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\acknowledgement{https://quadbase.org/questions/q14432v1}
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\begin{document}
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\begin{hint}
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This is an antiderivative problem. We wish to find the most general
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function $f(x)$ such that $f'(x) = 2e^{4x}$.
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This is an antiderivative problem. We wish to find the most general
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function $f(x)$ such that $f'(x) = 2e^{4x}$.
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\end{hint}
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% Update hint to fix bad notation issues
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\begin{hint}
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Try to guess an antiderivative.
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\[\int 2e^{4x}\; dx \approx e^{4x}+C.\]
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Try to guess an antiderivative.
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We know an antiderivative of $e^{4x}$ should be something like $e^{4x}$.
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Differentiate your guess.
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\[(e^{4x})'= 4e^{4x}.\]
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\end{hint}
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\begin{hint}
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Differentiate your guess.
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\[(e^{4x}+C)'= 4e^{4x}.\]
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Move the constant multiple $4$ to the other side by multiplying both sides by the constant $\dfrac{1}{4}$.
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\end{hint}
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\begin{hint}
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We are off by a factor of $\frac{1}{2}$.
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Multiply your guess by that factor.
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\end{hint}
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\begin{multipleChoice}
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\choice{$2e^{4x}+C$}
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\choice{$8e^{4x}+C$}
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\choice{$8e^{4x}$}
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\choice{$2e^{4x}$}
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\choice[correct]{$\frac{1}{2}e^{4x}+C$}
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\choice{$2e^{4x}+C$}
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\choice{$8e^{4x}+C$}
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\choice{$8e^{4x}$}
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\choice{$2e^{4x}$}
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\choice[correct]{$\frac{1}{2}e^{4x}+C$}
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\end{multipleChoice}
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\end{exercise}

‎antiderivatives/exercises/q14434v1.tex

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\documentclass{ximera}
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\input{../../preamble.tex}
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\author{Emma Smith Zbarsky\and Nela Lakos}
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\author{Emma Smith Zbarsky\and Nela Lakos \and Bobby Ramsey}
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\license{Creative Commons Attribution 3.0 Unported}
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\acknowledgement{https://quadbase.org/questions/q14434v1}
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\begin{document}
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Find the antiderivative: \[\int \left(6e^{3r} +12r^3 -5\right)\; dr\]
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\begin{hint}
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Apply the Sum Rule for antiderivatives.
14-
\[\int \left(6e^{3r} +12r^3 -5\right)\; dr=\int 6e^{3r}\; dr +\int12r^3\; dr+ \int(-5)\; dr\]
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Apply the Sum Rule for antiderivatives.
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\[\int \left(6e^{3r} +12r^3 -5\right)\; dr=\int 6e^{3r}\; dr +\int12r^3\; dr+ \int(-5)\; dr\]
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\end{hint}
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\begin{hint}
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Apply the Constant Multiple Rule for antiderivatives.
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\[\int \left(6e^{3r} +12r^3 -5\right)\; dr=\int 6e^{3r}\; dr +\int12r^3\; dr+ \int(-5)\; dr=6\int e^{3r}\; dr +12\int r^3\; dr-5 \int\; dr\]
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Apply the Constant Multiple Rule for antiderivatives.
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\[\int \left(6e^{3r} +12r^3 -5\right)\; dr=\int 6e^{3r}\; dr +\int12r^3\; dr+ \int(-5)\; dr=6\int e^{3r}\; dr +12\int r^3\; dr-5 \int\; dr\]
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\end{hint}
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\begin{hint}
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Guess an antiderivative.
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\[\int e^{3r}\; dr \approx e^{3r}+C \]
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Then differentiate it, and multiply by a factor, if needed.
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Guess an antiderivative.
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An antiderivative of $\displaystyle e^{3r}$ should be something like $e^{3r}$.
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Then differentiate it, and multiply by a factor, if needed.
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\end{hint}
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\begin{multipleChoice}
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\choice{$18e^{3r}+36r^2$}
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\choice{$3e^{3r}+4r^4-5r+C$}
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\choice{$3e^{3r}+4r^4-5r$}
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\choice{$2e^{3r}+3r^4-5r$}
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\choice[correct]{$2e^{3r}+3r^4-5r+C$}
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\choice{$18e^{3r}+36r^2$}
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\choice{$3e^{3r}+4r^4-5r+C$}
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\choice{$3e^{3r}+4r^4-5r$}
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\choice{$2e^{3r}+3r^4-5r$}
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\choice[correct]{$2e^{3r}+3r^4-5r+C$}
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\end{multipleChoice}
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\end{exercise}

‎applicationsOfIntegrals/exercises/additionalList.tex

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\documentclass{xourse}
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\input{../../preamble.tex}
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\begin{document}
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\part{Applications of integrals}
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% \practice{averageValue1.tex}
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% \practice{averageValue2.tex}
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% \practice{averageValue4.tex}
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% \practice{averageValue6.tex}
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% \practice{05_02_ex_16.tex}
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% \practice{applicationsOfIntegrals1.tex}
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% \practice{applicationsOfIntegrals2.tex}
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% \practice{applicationsOfIntegrals3.tex}
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% \practice{applicationsOfIntegrals4.tex}
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% \practice{applicationsOfIntegrals5.tex}
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% \practice{applicationsOfIntegrals6.tex}
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% \practice{applicationsOfIntegrals7.tex}
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% \practice{applicationsOfIntegrals8.tex}
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\practice{applicationsOfIntegrals9.tex}
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% \practice{applicationsOfIntegrals10.tex}
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% \practice{applicationsOfIntegrals11.tex}
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% \practice{applicationsOfIntegrals12.tex}
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\practice{averageValue5.tex}
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\end{document}

‎applicationsOfIntegrals/exercises/applicationsOfIntegrals11.tex

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%\outcome{Understand the difference between displacement and distance traveled.}
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%\outcome{Understand the relationship between position, velocity and acceleration.}
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\author{Nela Lakos \and Kyle Parsons}
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\author{Nela Lakos \and Kyle Parsons \and Bobby Ramsey}
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\begin{document}
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\begin{exercise}
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\[
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\int_0^1 x\cos\left(\frac{\pi}{2}x^2\right) \d x = \answer{\frac{1}{\pi}}
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\]
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\begin{hint}
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What is the derivative of $\sin\left(\frac{\pi}{2}x\right)$?
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\end{hint}
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\end{exercise}
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\end{document}

‎applicationsOfIntegrals/exercises/applicationsOfIntegrals5.tex

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Consider a particle moving along a line with acceleration and initial velocity given by
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\begin{align*}
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a(t) &= 1-2t\\
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v(0) &= 6
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a(t) &= 1-2t\\
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v(0) &= 6
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\end{align*}
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for $0\leq t\leq4$.
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v(t) = \answer{6-t^2+t}.
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\]
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The total \emph{distance} that the particle travels on the interval $[0,4]$ is $\answer{\frac{49}{3}}$.
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The \emph{total distance} that the particle travels on the interval $[0,4]$ is $\answer{\frac{49}{3}}$.
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\begin{hint}
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Note
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\[
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v(t)=-(t-3)(t+2).
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\]
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Note $\displaystyle v(t)=-(t-3)(t+2)$
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Therefore, $v$ is positive on $[0,3)$ and negative on $(3,4]$.
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\end{hint}
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\end{exercise}

‎applicationsOfIntegrals/exercises/averageValue1.tex

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\documentclass{ximera}
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\input{../../preamble.tex}
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\author{Steven Gubkin\and Nela lakos}
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\author{Steven Gubkin\and Nela Lakos \and Bobby Ramsey}
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\license{Creative Commons 3.0 By-NC}
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\begin{document}
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\begin{exercise}
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Find the average value of $f(x)=e^x$ on the interval $[\ln(2),\ln(8)]$.
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\begin{hint}
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Just apply the formula:
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$\overline{f}=\frac{1}{\ln(8)-\ln(2)}\int_{\ln(2)}^{\ln(8) }f(x)\d x$
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Apply the formula for the average value:
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$\overline{f}=\frac{1}{\ln(8)-\ln(2)}\int_{\ln(2)}^{\ln(8) }f(x)\d x$
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\end{hint}
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\begin{hint}
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Remember to simplify:
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\[
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\ln(8)-\ln(2)=\ln\left(\frac{8}{2}\right)=\ln(4)=\ln(2^2)=2\ln (2)
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\]
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For the denominator, notice that you can simplify:
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\[
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\ln(8)-\ln(2)=\ln\left(\frac{8}{2}\right)=\ln(4)=\ln(2^2)=2\ln (2)
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\]
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\end{hint}
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\begin{prompt}
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\[
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\overline{f}=\frac{\answer{3}}{\ln(2)}
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\]
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\[
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\overline{f}=\frac{\answer{3}}{\ln(2)}
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\]
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\end{prompt}
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\end{exercise}

‎applicationsOfIntegrals/exercises/exerciseList.tex

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\begin{document}
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\part{Applications of integrals}
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\practice{averageValue1.tex}
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\practice{averageValue2.tex}
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\practice{averageValue4.tex}
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\practice{averageValue6.tex}
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\practice{05_02_ex_16.tex}
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\practice{applicationsOfIntegrals1.tex}
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\practice{applicationsOfIntegrals2.tex}
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\practice{applicationsOfIntegrals3.tex}
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\practice{applicationsOfIntegrals4.tex}
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\practice{applicationsOfIntegrals5.tex}
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\practice{applicationsOfIntegrals6.tex}
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\practice{applicationsOfIntegrals7.tex}
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\practice{applicationsOfIntegrals8.tex}
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\practice{applicationsOfIntegrals9.tex}
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\practice{applicationsOfIntegrals10.tex}
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\practice{applicationsOfIntegrals11.tex}
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\practice{applicationsOfIntegrals12.tex}
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\practice{averageValue5.tex}
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\practice{averageValue1.tex}
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\practice{averageValue2.tex}
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\practice{averageValue4.tex}
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\practice{averageValue6.tex}
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\practice{05_02_ex_16.tex}
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\practice{applicationsOfIntegrals1.tex}
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\practice{applicationsOfIntegrals2.tex}
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\practice{applicationsOfIntegrals3.tex}
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\practice{applicationsOfIntegrals4.tex}
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\practice{applicationsOfIntegrals5.tex}
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\practice{applicationsOfIntegrals6.tex}
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\practice{applicationsOfIntegrals7.tex}
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\practice{applicationsOfIntegrals8.tex}
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% \practice{applicationsOfIntegrals9.tex}
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\practice{applicationsOfIntegrals10.tex}
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\practice{applicationsOfIntegrals11.tex}
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\practice{applicationsOfIntegrals12.tex}
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% \practice{averageValue5.tex}
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\end{document}

‎approximatingTheAreaUnderACurve/exercises/additionalList.tex

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\documentclass{xourse}
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\input{../../preamble.tex}
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\begin{document}
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\part{Approximating the area under a curve}
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% \practice{q14596v1.tex}
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\practice{q15551v1.tex}
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% \practice{05_03_ex_05.tex}
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% \practice{05_03_ex_06.tex}
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% \practice{05_03_ex_07.tex}
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% \practice{05_03_ex_08.tex}
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% \practice{05_03_ex_09.tex}
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% \practice{05_03_ex_10.tex}
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% \practice{05_03_ex_16.tex}
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% \practice{05_03_ex_17.tex}
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% \practice{05_03_ex_25.tex}
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% \practice{riemannSum1.tex}
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% \practice{riemannSum3.tex}
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% \practice{riemannSum2.tex}
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% \practice{limitOfRiemannSums.tex}
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\end{document}

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