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author | Karl Berry <karl@freefriends.org> | 2017-03-16 21:43:23 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2017-03-16 21:43:23 +0000 |
commit | 963f87c9830b8a8617be166bc065fbfb21223f86 (patch) | |
tree | 82f2f0bc099c0f65a71d391c759b5df75a57d398 /Master/texmf-dist/doc/latex/studenthandouts/samplecode | |
parent | 3ab47cf457a56372d1185ab7990bd2035d6f5754 (diff) |
studenthandouts (16mar17)
git-svn-id: svn://tug.org/texlive/trunk@43516 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/studenthandouts/samplecode')
8 files changed, 355 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/studenthandouts/samplecode/worksheets.tex b/Master/texmf-dist/doc/latex/studenthandouts/samplecode/worksheets.tex new file mode 100644 index 00000000000..94895708de9 --- /dev/null +++ b/Master/texmf-dist/doc/latex/studenthandouts/samplecode/worksheets.tex @@ -0,0 +1,73 @@ +\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/Master/texmf-dist/doc/latex/studenthandouts/samplecode/worksheets/handout-1-1.tex b/Master/texmf-dist/doc/latex/studenthandouts/samplecode/worksheets/handout-1-1.tex new file mode 100644 index 00000000000..3e048696071 --- /dev/null +++ b/Master/texmf-dist/doc/latex/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/Master/texmf-dist/doc/latex/studenthandouts/samplecode/worksheets/handout-1-2.tex b/Master/texmf-dist/doc/latex/studenthandouts/samplecode/worksheets/handout-1-2.tex new file mode 100644 index 00000000000..c106d6a68c6 --- /dev/null +++ b/Master/texmf-dist/doc/latex/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/Master/texmf-dist/doc/latex/studenthandouts/samplecode/worksheets/handout-1-3.tex b/Master/texmf-dist/doc/latex/studenthandouts/samplecode/worksheets/handout-1-3.tex new file mode 100644 index 00000000000..b8cd8f15c67 --- /dev/null +++ b/Master/texmf-dist/doc/latex/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/Master/texmf-dist/doc/latex/studenthandouts/samplecode/worksheets/handout-2-1.tex b/Master/texmf-dist/doc/latex/studenthandouts/samplecode/worksheets/handout-2-1.tex new file mode 100644 index 00000000000..4c03b10083e --- /dev/null +++ b/Master/texmf-dist/doc/latex/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/Master/texmf-dist/doc/latex/studenthandouts/samplecode/worksheets/handout-2-2.tex b/Master/texmf-dist/doc/latex/studenthandouts/samplecode/worksheets/handout-2-2.tex new file mode 100644 index 00000000000..4e93aa48fe7 --- /dev/null +++ b/Master/texmf-dist/doc/latex/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/Master/texmf-dist/doc/latex/studenthandouts/samplecode/worksheets/handout-3-1.tex b/Master/texmf-dist/doc/latex/studenthandouts/samplecode/worksheets/handout-3-1.tex new file mode 100644 index 00000000000..0bb90e4ec67 --- /dev/null +++ b/Master/texmf-dist/doc/latex/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/Master/texmf-dist/doc/latex/studenthandouts/samplecode/worksheets/handout-3-2.tex b/Master/texmf-dist/doc/latex/studenthandouts/samplecode/worksheets/handout-3-2.tex new file mode 100644 index 00000000000..6d5cefe0a8e --- /dev/null +++ b/Master/texmf-dist/doc/latex/studenthandouts/samplecode/worksheets/handout-3-2.tex @@ -0,0 +1,48 @@ +\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} + + + + |