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authorNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
committerNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
commite0c6872cf40896c7be36b11dcc744620f10adf1d (patch)
tree60335e10d2f4354b0674ec22d7b53f0f8abee672 /macros/latex/contrib/studenthandouts/samplecode
Initial commit
Diffstat (limited to 'macros/latex/contrib/studenthandouts/samplecode')
-rw-r--r--macros/latex/contrib/studenthandouts/samplecode/worksheets.tex73
-rw-r--r--macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-1-1.tex44
-rw-r--r--macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-1-2.tex38
-rw-r--r--macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-1-3.tex23
-rw-r--r--macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-2-1.tex55
-rw-r--r--macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-2-2.tex26
-rw-r--r--macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-3-1.tex48
-rw-r--r--macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-3-2.tex48
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diff --git a/macros/latex/contrib/studenthandouts/samplecode/worksheets.tex b/macros/latex/contrib/studenthandouts/samplecode/worksheets.tex
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+\documentclass[10pt,oneside,letterpaper]{article}
+
+\usepackage{studenthandouts}
+
+
+
+\title{Sample Student Handouts output}
+\author{James Fennell}
+
+\begin{document}
+
+
+\maketitle
+
+
+\noindent
+This is a sample collection of student worksheets compiled using the Student Handouts package.
+ In this sample project there are seven underlying handouts -- 1.1, 1.2, 1.3, 2.1, 2.2, 3.1, and 3.2 --
+ but not all are compiled initially in order to illustrate the functionality of the handout import management commands.
+
+Some of the handouts contain the output of \verb$\allhandoutinfo$.
+ This is to show you the specific handout information that can be used when styling the handouts.
+This information can also be used in the handouts themselves, as here.
+
+If you wish to use the package, one option would be to copy the sample code over and use that as the basis for your project.
+ However, as you will see from looking at the sample code itself, very little is required to get a handouts project up and running from scratch.
+
+\vspace{\baselineskip}
+\noindent
+Regarding formatting: the sample handouts here illustrate two possibilities in terms of the function of a handout.
+ The handouts in unit 1 are meant to be written on by students, whereas the handouts in units 2 and 3 are not.
+ The unit 1 handouts do this by judicious use of the \verb$\vfill$ command which spreads the questions evenly down the page.
+ Inspecting the source will make it clear how this is done.
+
+
+
+
+\tableofcontents
+
+
+
+\renewcommand{\thehandoutsdirectory}{worksheets/}
+\renewcommand{\thehandoutscredit}{NYU Calculus 1 Summer 2015}
+
+\setunittitle{1}{Introduction to Differentiation}
+\setunittitle{3}{Advanced Differentiation}
+
+
+\importhandout{1}{1}
+\importhandout{1}{2}
+\importhandout{1}{3}
+\importhandout{2}{1}
+
+
+% Some random handout import management instructions.
+% Note that 2.2 will not be imported. Even though 2.2 is in the list of admissible handouts, its unit is not in the list of admissible units.
+\importonlyunits{3}
+\importonlyhandouts{2.2,3.2}
+
+
+\importhandout{2}{2}
+\importhandout{3}{1}
+\importhandout{3}{2}
+
+
+
+
+\end{document}
+
+
+
+
+
diff --git a/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-1-1.tex b/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-1-1.tex
new file mode 100644
index 0000000000..3e04869607
--- /dev/null
+++ b/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-1-1.tex
@@ -0,0 +1,44 @@
+\sethandouttitle{From First Principles}
+
+
+
+\allhandoutinfo{}
+
+\begin{enumerate}
+ \item Find the equation of the tangent line to the curves
+ \begin{enumerate}
+ \item $y=4x-3x^2$ ar $(2,-4)$.
+ \vfill
+ \item $y = \sqrt{x}$ at $(1,1)$.
+ \vfill
+ \end{enumerate}
+
+ \item The displacement of a particle moving in a straight line is given by the equation of motion $s=1/t^2$.
+ Find the velocity of the particle at $t=a$, $t=1$, $t=2$ and $t=3$.
+
+ \vfill
+ \newpage
+
+ \item Each limit represents the derivative of some function $f$ at a number $a$. State such an $f$ and $a$ in each case.
+ \begin{enumerate}
+ \item $\displaystyle\lim_{h \rightarrow 0} \frac{ (1+h)^8 - 1 }{h}$.
+ \vfill
+ \item $\displaystyle\lim_{x \rightarrow 5} \frac{ 2^x - 32}{x-5}$.
+ \vfill
+ \item $\displaystyle\lim_{h \rightarrow 0} \frac{ \cos(\pi + h) + 1 }{h}$.
+ \vfill
+ \end{enumerate}
+
+ \newpage
+ \item The cost in dollars of producing $x$ units of a certain commodity is $C(x)= 500 + 10x + 0.05 x^2$.
+ \begin{enumerate}
+ \item Find the average rate of change of $C$ with respect to $x$ when the production level is changed
+ from $x=100$ to $x=105$.
+ \vfill
+ \item Find the average rate of change of $C$ with respect to $x$ when the production level is changed
+ from $x=100$ to $x=101$.
+ \vfill
+ \item Find the instantaneous rate of change of $C$ with respect to $x$ when $x=100$.
+ \vfill
+ \end{enumerate}
+\end{enumerate}
diff --git a/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-1-2.tex b/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-1-2.tex
new file mode 100644
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--- /dev/null
+++ b/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-1-2.tex
@@ -0,0 +1,38 @@
+\sethandouttitle{}
+
+
+\begin{enumerate}
+ \item Differentiate the function.
+ \begin{enumerate}
+ \item $f(x) = x^3 - 4x+6$.
+ \vfill
+ \item $f(s) = \frac{-12}{s^5} + \sin(s)$.
+ \vfill
+ \item $f(x) = \frac{ x^2 + 4x + 3 }{\sqrt{x}}$.
+ \vfill
+ \end{enumerate}
+
+ \item Find an equation for the tangent line of $y=3x^2 - x^3$ at $(1,2)$.
+ \vfill
+
+ \newpage
+
+ \item Find the first and second derivatives of $f(x) = x^4 - 3x^3 + 16x$.
+ \vfill
+
+ \item The position function of a particle is given by $s = t^3 - 4.5 t^2 - 7t$, $t \geq 0$.
+ \begin{enumerate}
+ \item When does the particle reach a velocity of 5m/s?
+ \vfill
+ \item When is the acceleration 0? What is the signifigance of this value of $t$?
+ \vfill
+ \end{enumerate}
+
+ \item A spherical balloon is being inflated.
+ Find the rate of increase of the surface area ($S= 4 \pi r^2$)
+ with respect to the radius when $r=1$, $r=2$ and $r=3$. What conclusion can you make?
+ \vfill
+\end{enumerate}
+
+\allhandoutinfo
+
diff --git a/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-1-3.tex b/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-1-3.tex
new file mode 100644
index 0000000000..b8cd8f15c6
--- /dev/null
+++ b/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-1-3.tex
@@ -0,0 +1,23 @@
+\sethandouttitle{The Product Rule}
+
+
+
+\begin{enumerate}
+ \item Find the derivative of $f(x) = (1+2x^2)(x-x^2)$ in two ways: by using the Product Rule and
+ by performing the multiplication first. Do your answers agree?
+ \vfill
+
+ \item Differentiate the function.
+ \begin{enumerate}
+ \item $f(x) = t^3 \cos(t)$.
+ \vfill
+ \item $f(x) = \sin(x) \cos(x)$.
+ \vfill
+ \end{enumerate}
+
+ \item If $f$ is a differentiable function find an expresion for the derivative of $y = x^2 f(x)$.
+ \vfill
+
+\end{enumerate}
+
+
diff --git a/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-2-1.tex b/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-2-1.tex
new file mode 100644
index 0000000000..4c03b10083
--- /dev/null
+++ b/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-2-1.tex
@@ -0,0 +1,55 @@
+\sethandouttitle{The Exponential and Logarithm Functions}
+
+
+\begin{enumerate}
+
+ \item Evaluate $f(x) = x^2$ and $g(x) = 2^x$ at $x=-3,-2,-1,0,1,2,3,4,5$. Graph both functions on the same graph.
+
+ \item Find the domain of $\displaystyle f(x) = \frac{ 1 - e^{x^2} }{ 1 - e^{1-x^2} }$ and $\displaystyle g(x) = \frac{ 1+x }{ e^{\cos x} }$.
+
+ \item Find the limit.
+ \begin{enumerate}
+ \item $\displaystyle\lim_{ x \rightarrow \infty } (1.0001)^x $.
+ \item $\displaystyle\lim_{x \rightarrow \infty} \frac{ e^{3x} - e^{-3x} }{ e^{3x} + e^{-3x} }$.
+ \item $\displaystyle \lim_{x \rightarrow \infty} ( e^{-2x} \cos x)$.
+ \end{enumerate}
+
+ \item Is $g(x) = 1/x$ one-to-one?
+
+ \item If $g(x) = 3 +x + e^x$, find $g^{-1}(4)$.
+
+ \newpage
+
+ \item The formula $C = \frac{5}{9}(F-32)$ expresses Celsius $C$ as a function of Fahrenheit $F$.
+ Find a formula for the inverse function and interpret it.
+
+ \item Find the inverse of the function $f(x) = 1 + \sqrt{ 2 + 3x }$.
+
+ \item Find the inverse of the function $f(x) = e^{2x-1}$.
+
+ \item Find $ (f^{-1})'(a)$ using the inverse derivative formula.
+ \begin{enumerate}
+ \item $f(x) = x^3$.
+ \item $f(x) = 9-x^2$.
+ \end{enumerate}
+ Then, find the inverse function first and differentiate it. Do your answers agree?
+
+
+ \item Find the exact value of each expression (without a calculator).
+ \begin{enumerate}
+ \item $\log_5(125)$.
+ \item $\displaystyle \log_3\left( \frac{1}{27} \right)$.
+ \item $\log_2 6 - \log_2 15 + \log_2 20$.
+ \end{enumerate}
+
+ \item Solve for $x$:
+ \begin{enumerate}
+ \item $e^{7-4x}=6$.
+ \item $\ln(3x-10) = 2$.
+ \item $\ln x + \ln (x-1) = 1$.
+ \end{enumerate}
+
+\end{enumerate}
+
+
+
diff --git a/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-2-2.tex b/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-2-2.tex
new file mode 100644
index 0000000000..4e93aa48fe
--- /dev/null
+++ b/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-2-2.tex
@@ -0,0 +1,26 @@
+\sethandouttitle{Trignometric Functions}
+
+\begin{enumerate}
+
+ \item Differentiate the function.
+ \begin{enumerate}
+ \item $f(x) = \sin(\ln x)$.
+ \item $f(x) = \sin(x) \ln(5x)$.
+ \item $g(x) = \ln\left( \frac{ (2y+1)^5 }{ \sqrt{ y^2+1} } \right)$.
+ \item $y = \frac{x}{e^x}$.
+ \item $F(t) = e^{t \sin(2t) }$.
+ \end{enumerate}
+
+ \item Without simplfiying, find the derivative of $f(x) = \ln( e^{3x} )$.
+ Then simply $f(x)$ and differentiate. Do your answers agree?
+
+ \item Use logarithmic differentiation to differentiate the function.
+ \begin{enumerate}
+ \item $f(x) = (x^2+2)^2(x^4+4)^4$.
+ \item $f(x) = x^x$.
+ \end{enumerate}
+
+
+\end{enumerate}
+
+
diff --git a/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-3-1.tex b/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-3-1.tex
new file mode 100644
index 0000000000..0bb90e4ec6
--- /dev/null
+++ b/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-3-1.tex
@@ -0,0 +1,48 @@
+\sethandouttitle{Maximum and Minimum Values}
+
+\allhandoutinfo{}
+
+\begin{enumerate}
+
+
+ \item Sketch the graph of a function $f$ that is continous on $[1,5]$ and has an absolute minimum at 2,
+ absolute maximum at 3, and a local minimum at 4.
+
+ \item \begin{enumerate}
+ \item Sketch the graph of a function that has a local maximum at 2 and is differentiable at 2.
+ \item Sketch the graph of a function that has a local maximum at 2 and is continuous but not differentiable at 2.
+ \item Sketch the graph of a function that has a local maximum at 2 and is not continuous at 2.
+ \end{enumerate}
+
+
+ \item Sketch the graph of $f$ and use your sketch to find the absolute and local maximum and minimum values of $f$.
+ \begin{enumerate}
+ \item $\displaystyle f(x) = \frac{1}{2}(3x-1), \quad x \leq 3$.
+ \item $f(x) = \sin(x), \quad 0 \leq x < \pi/2$.
+ \item $f(x) = \ln(x), \quad 0<x \leq 2$.
+ \item $f(x) = 1 - \sqrt{x}$.
+ \end{enumerate}
+
+ \item Find the critical numbers of the function.
+ \begin{enumerate}
+ \item $\displaystyle f(x) = 4+ \frac{1}{3}x - \frac{1}{2}x^2$.
+ \item $\displaystyle g(y) = \frac{y-1}{ y^2 - y + 1 }$.
+ \item $f(\theta) = 2 \cos \theta + \sin^2 \theta$.
+ \item $f(\theta) = x^2 e^{-3x}$.
+ \end{enumerate}
+
+ \item Find the absolute maximum and minimum values of $f$ on the given interval.
+ \begin{enumerate}
+ \item $f(x) = 12+4x-x^2$ on $[0,5]$.
+ \item $f(t) = t \sqrt{4-t^2}$ on $[-1,2]$.
+ \item $f(t) = 2 \cos t + \sin 2t$ on $[0,\pi/2]$.
+ \item $f(x) = x e^{-x^2/8}$ on $[-1,4]$.
+ \item $f(x) = \ln(x^2+x+1)$ on $[-1,1]$.
+ \end{enumerate}
+
+
+
+\end{enumerate}
+
+
+
diff --git a/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-3-2.tex b/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-3-2.tex
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+++ b/macros/latex/contrib/studenthandouts/samplecode/worksheets/handout-3-2.tex
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+\sethandouttitle{The Mean Value Theorem}
+
+
+\begin{enumerate}
+
+
+ \item Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.
+ Then find all numbers $c$ that satisfy the conclusion of Rolle's Theorem.
+ \begin{enumerate}
+ \item $f(x) = 5 - 12x + 3x^2$ on $[1,3]$.
+ \item $f(x) = \sqrt{x} - \frac{1}{3}x$ on $[0,9]$.
+ \end{enumerate}
+
+ \item Let $f(x) = 1 - x^{2/3}$. Show that $f(-1)=f(1)$ but there is no number $c$ in $(-1,1)$ such that $f'(c)=0$.
+ Why does this not contradict Rolle's Theorem?
+
+ \item Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval.
+ Then find all numbers $c$ that satisfy the conclusion of the Mean Value Theorem.
+ \begin{enumerate}
+ \item $f(x) = 2x^2 - 3x +1$ on $[0,2]$.
+ \item $f(x) = \ln(x)$ on $[1,4]$.
+ \end{enumerate}
+
+ \item Let $f(x) = 2 - |2x-1|$. Show that there is no value of $c$ such that
+ \[
+ f(3)-f(0) = f'(c)(3-0).
+ \]
+ Why does this not contradict the Mean Value Theorem?
+
+ \item Show that the equation $2x + \cos(x)$ has exactly one real root.
+
+ \item If $f(1)=10$ and $f'(2) \geq 2$ for $1 \leq x \leq 4$, how small can $f(4)$ possibly be?
+
+ \item Does there exist a function $f$ such that $f(0) = -1$, $f(2) = 4$ and $f'(x) \leq 2$?
+
+
+ \item Prove that
+ \[
+ \arcsin \left( \frac{x-1}{x+1} \right) = 2 \arctan \sqrt{x} - \frac{\pi}{2}.
+ \]
+
+
+
+\end{enumerate}
+
+
+
+