From 6f01e99cb7175030ab6087251677b5b4a5356deb Mon Sep 17 00:00:00 2001 From: Greg Hartman Date: Mon, 22 Jan 2018 17:51:55 -0500 Subject: [PATCH] fixes through error (236) --- _CalculusFix.answers | 2 +- _CalculusFix.pdf | Bin 568123 -> 745599 bytes _CalculusFix.tex | 24 ++++++++++++------------ _ErrorList.tex | 19 +++++++++++++++++++ exercises/02_01_ex_33.tex | 2 +- text/08_Alternating_Series.tex | 2 +- text/08_Sequences.tex | 2 +- text/08_Series.tex | 4 ++-- 8 files changed, 37 insertions(+), 18 deletions(-) diff --git a/_CalculusFix.answers b/_CalculusFix.answers index 245d7af..e9f0bc6 100644 --- a/_CalculusFix.answers +++ b/_CalculusFix.answers @@ -3,5 +3,5 @@ \noindent {\Large \bf Chapter 1} \vskip \baselineskip \noindent {\bf Section 1.1} \vskip \baselineskip -\printanswers {exercises/09_05_exercises} +\printanswers {exercises/11_01_exercises} \end {multicols}\normalsize diff --git a/_CalculusFix.pdf b/_CalculusFix.pdf index 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L(9+7P%c1-aR*A 2, this limit is not defined. +% 1/22/18 already done (222) Page 37 has a grammatical error. The sentence should say: (223) We have seen, though, that this is not necessarily a good indicator (224) of what f(x) actually is. +% 1/22/18 already fixed (225) Error on page 200 (226) Message: The sentence (227) "Finally, we find the total signed area under the velocity function from t=0 to t=2 to find the s(2), the height at t=2, which is a displacement, the distance from the current position to the starting position" is an awkward, unclear, run-on sentence. Something like (228) "Finally, to find the height of the object at time t=2 we calculate the total signed area under the velocity function from t=0 to t=2. This signed area is equal to s(2), the displacement (i.e., signed distance) from the starting position at t=0 to the position at time t=2." (229) would be an improvement. Note that in the proposed revision, it is emphasized that displacement is a signed distance. +% 1/18/22 Already fixed; my guess is this was done before mbx was started (230) Message: Page 319 (231) Section 6.6 Hyperbolic Functions (232) Key Idea 19 (233) Item #3 The factor in front of ln should be 1/(2a) +% 1/22/18 done + + (234) Subject: error on p. 624 (235) Message: I and my students are liking using APEX Calculus 3.0 for Multivariable Calculus at Alverno College. (236) There appears to be an error in Figure 11.3 on p. 624. The figure claims to be showing the graph of a vector valued function defined in Example 357, and "its derivative at one point." In fact, the derivative has not yet been defined, and what is being shown is the vector at a point. +% 1/18/22 already fixed (237) One typo in Version 3 - page 416, Example 239, 5, the index of the series should probably start at 11 instead of 10. diff --git a/exercises/02_01_ex_33.tex b/exercises/02_01_ex_33.tex index 17268b7..3c76e5b 100644 --- a/exercises/02_01_ex_33.tex +++ b/exercises/02_01_ex_33.tex @@ -17,6 +17,6 @@ \item $(-\infty,\infty)$ \item $(-\infty,-1)\cup (-1,1) \cup (1,\infty)$ \item $(-\infty,5]$ -\item $[-5,5]$ +\item $[-\sqrt{5},\sqrt{5}]$ \end{enumerate} } diff --git a/text/08_Alternating_Series.tex b/text/08_Alternating_Series.tex index 9787ff4..de8debb 100644 --- a/text/08_Alternating_Series.tex +++ b/text/08_Alternating_Series.tex @@ -85,7 +85,7 @@ \section{Alternating Series and Absolute Convergence}\label{sec:alt_series} \noindent$\ds 1.\ \sum_{n=1}^\infty (-1)^{n+1}\frac{1}{n^3}\qquad 2.\ \sum_{n=1}^\infty (-1)^{n+1}\frac{\ln n}{n}$. } {\begin{enumerate} - \item Using Theorem \ref{thm:alt_series_approx}, we want to find $n$ where $1/n^3 < 0.001$: + \item Using Theorem \ref{thm:alt_series_approx}, we want to find $n$ where $1/n^3 \leq 0.001$: \begin{align*} \frac1{n^3} &\leq 0.001=\frac{1}{1000} \\ n^3 &\geq 1000\\ diff --git a/text/08_Sequences.tex b/text/08_Sequences.tex index d23ad8e..cc7aab2 100644 --- a/text/08_Sequences.tex +++ b/text/08_Sequences.tex @@ -271,7 +271,7 @@ \section{Sequences}\label{sec:sequences} There is more to learn about sequences than just their limits. We will also study their range and the relationships terms have with the terms that follow. We start with some definitions describing properties of the range. \definition{def:bounded}{Bounded and Unbounded Sequences} -{A sequence $\{a_n\}$ is said to be \textbf{bounded} if there exists real numbers $m$ and $M$ such that $m < a_n < M$ for all $n$ in $\mathbb{N}$.\\ +{A sequence $\{a_n\}$ is said to be \textbf{bounded} if there exist real numbers $m$ and $M$ such that $m < a_n < M$ for all $n$ in $\mathbb{N}$.\\ A sequence $\{a_n\}$ is said to be \textbf{unbounded} if it is not bounded.\\ diff --git a/text/08_Series.tex b/text/08_Series.tex index 5aef731..270ce64 100644 --- a/text/08_Series.tex +++ b/text/08_Series.tex @@ -226,7 +226,7 @@ \section{Infinite Series}\label{sec:series} \mfigure{.75}{Scatter plots relating to the series of Example \ref{ex_series3}.}{fig:series3}{figures/figseries3} }\\ -The series in Example \ref{ex_series3} is an example of a \sword{telescoping series}. Informally, a telescoping series is one in which the partial sums reduce to just a finite number of terms. The partial sum $S_n$ did not contain $n$ terms, but rather just two: 1 and $1/(n+1)$.\index{series!telescoping}\index{telescoping series} +The series in Example \ref{ex_series3} is an example of a \sword{telescoping series}. Informally, a telescoping series is one in which most terms cancel with preceding or following terms, reducing the number of terms in each partial sum. The partial sum $S_n$ did not contain $n$ terms, but rather just two: 1 and $1/(n+1)$.\index{series!telescoping}\index{telescoping series} When possible, seek a way to write an explicit formula for the $n^\text{th}$ partial sum $S_n$. This makes evaluating the limit $\ds\lim_{n\to\infty} S_n$ much more approachable. We do so in the next example.\\ @@ -392,7 +392,7 @@ \section{Infinite Series}\label{sec:series} \textbf{Important!} This theorem \emph{does not state} that if $\ds \lim_{n\to\infty} a_n = 0$ then $\ds \sum_{n=1}^\infty a_n $ converges. The standard example of this is the Harmonic Series, as given in Key Idea \ref{idea:famous_series}. The Harmonic Sequence, $\{1/n\}$, converges to 0; the Harmonic Series, $\ds \sum_{n=1}^\infty 1/n$, diverges. \theorem{thm:series_behavior}{Infinite Nature of Series} -{The convergence or divergence remains unchanged by the addition or subtraction of any finite number of terms. That is: +{The convergence or divergence of an infinite series remains unchanged by the addition or subtraction of any finite number of terms. That is: \begin{enumerate} \item A divergent series will remain divergent with the addition or subtraction of any finite number of terms. \item A convergent series will remain convergent with the addition or subtraction of any finite number of terms. (Of course, the \emph{sum} will likely change.)

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