evens out exercises through chapter 5

_CalculusFix.answers

@@ -3,5 +3,7 @@
 \noindent {\Large \bf Chapter 1} \vskip \baselineskip 
 \noindent {\bf Section 1.1} \vskip \baselineskip 
 
-\printanswers {exercises/02_07_exercises}
+\printanswers {exercises/05_01_exercises}
+\noindent {\bf Section 1.2} \vskip \baselineskip 
+\printanswers {exercises/05_05_exercises}
 \end {multicols}\normalsize 

_CalculusFix.tex

@@ -63,6 +63,10 @@
 %\printinblackandwhite
 \printallanswers
 
+%%\ifthenelse{\boolean{printquestions}}{\columnbreak}{}
+%5\ifthenelse{\boolean{printquestions}}{\vfill\null\columnbreak}{}
+
+
 
 %%\input{text/front_matter_and_coverI}
 
@@ -79,24 +83,24 @@
 %%
 %%%%\addtocounter{chapter}{1}
 %
-\clearpage{\pagestyle{empty}\cleardoublepage}
-\chapter{Derivatives}\label{chapter:derivatives}
-\thispagestyle{empty}
+%\clearpage{\pagestyle{empty}\cleardoublepage}
+%\chapter{Derivatives}\label{chapter:derivatives}
+%\thispagestyle{empty}
 %%
 %\input{text/02_Derivative}
 %\input{text/02_Derivative_Meaning}
 %\input{text/02_Derivative_Rules}
 %\input{text/02_Product_Quotient_Rules}
 %\input{text/02_Chain_Rule}
 %\input{text/02_Implicit_Differentiation}
-\input{text/02_Derivative_Inverse_Functions}
+%\input{text/02_Derivative_Inverse_Functions}
 %%%%
 %%%%\addtocounter{chapter}{2}
-%
+%%
 %\clearpage{\pagestyle{empty}\cleardoublepage}
 %\chapter{The Graphical Behavior of Functions}\label{chapter:graphbehavior}
 %\thispagestyle{empty}
-%
+
 %\input{text/03_Extreme_Values}
 %\input{text/03_Mean_Value_Theorem}
 %\input{text/03_Increasing_Decreasing}
@@ -133,17 +137,17 @@ \chapter{Derivatives}\label{chapter:derivatives}
 %%%%
 %%%%%\addtocounter{chapter}{4}
 %%
-%\clearpage{\pagestyle{empty}\cleardoublepage}
-%\chapter{Integration}\label{chapter:integration}
-%\thispagestyle{empty}
-%\addtocontents{toc}{\protect\thispagestyle{empty}}
+\clearpage{\pagestyle{empty}\cleardoublepage}
+\chapter{Integration}\label{chapter:integration}
+\thispagestyle{empty}
+\addtocontents{toc}{\protect\thispagestyle{empty}}
 
-%\input{text/05_Antiderivatives}
+\input{text/05_Antiderivatives}
 %\addtocontents{toc}{\protect\thispagestyle{empty}}
 %\input{text/05_Definite_Integral}
 %\input{text/05_Riemann_Sums}
 %\input{text/05_FTC}
-%\input{text/05_Numerical_Integration}
+\input{text/05_Numerical_Integration}
 %%%
 %%%%%%
 %%%%%%%

_ErrorList.tex

@@ -1011,6 +1011,20 @@
 % 2.5 added more chain rule problems
 % 2.6 added one more implicit dy/dx with graph. Lots of work!!
 % 2.7 actually removed a problem (old #27) to make a section have 2 problems instead of 3. If I added more, the HW page spilled into 2 pages.
+% 3.1 added terms and concepts q, along with another graphed problem
+% 3.3 added terms and concepts
+% 3.4 took out a problem - old #11, as concavity of sin x isn't much different than cos x
+%     Added a problem to each of the next 3 exsets, as they are all linked and had an odd # of problems.
+% 3.5 Added terms and concepts question, added problem at end (new #28)
+% 4.1 added a newton's method, 5 step problem
+% 4.4 added a terms and concepts question, reorganized some problems with exset
+% 5.1 added terms and concepts. An exset on antiderivs has an odd # of problems, but left it as it works out ok
+% 5.2 added problem about def. int. & geometry
+% 5.3 added two different summations questions in two diff. exsets
+% 5.4 added integration q about sin on interval of 2pi, added q about displacement given velocity function
+% 5.5 added one more term/concept q
+
+
 
 (262) Curve sketching. Include sketches by hand? If so, need BW versions, too.
 

exercises/03_01_ex_08.tex

@@ -2,7 +2,7 @@
 $\ds f(x) = \frac{2}{x^2+1}$
 
 \myincludegraphics[scale=.8]{figures/fig03_01_ex_08}
-\ifthenelse{\boolean{printquestions}}{\columnbreak}{}
+%\ifthenelse{\boolean{printquestions}}{\columnbreak}{}
 %\end{minipage}
 }
 {$\fp(0) = 0$

exercises/03_01_ex_25.tex

@@ -0,0 +1,8 @@
+{%\begin{minipage}{\linewidth}
+$\ds f(x) = \sqrt[3]{x^4-2x+1}$
+
+\myincludegraphics[scale=.8]{figures/fig03_01_ex_25}
+%\end{minipage}
+}
+{Both $\fp(-1)$ and $\fp(1)$ are undefined.
+}

exercises/03_01_ex_26.tex

@@ -0,0 +1,3 @@
+{Fill in the blanks: The critical points of a function $f$ are found where $\fp(x)$ is equal to \underline{\hskip.5in} or where $\fp(x)$ is \underline{\hskip.5in}.}
+{Where $\fp(x)$ is equal to \underline{0} or where $\fp(x)$ is \underline{undefined}.
+}

exercises/03_01_exercises.tex

@@ -4,8 +4,10 @@
 \exinput{exercises/03_01_ex_03}
 \exinput{exercises/03_01_ex_04}
 \exinput{exercises/03_01_ex_05}
+\exinput{exercises/03_01_ex_26}
 \printproblems
 \exsetinput{exercises/03_01_exset_01}
+\ifthenelse{\boolean{printquestions}}{\columnbreak}{}
 \exsetinput{exercises/03_01_exset_02}
 \exsetinput{exercises/03_01_exset_03}
 \printreview

exercises/03_01_exset_02.tex

@@ -4,6 +4,7 @@
 \exinput{exercises/03_01_ex_09}
 \exinput{exercises/03_01_ex_10}
 \exinput{exercises/03_01_ex_11}
+\exinput{exercises/03_01_ex_14}
+\exinput{exercises/03_01_ex_25}
 \exinput{exercises/03_01_ex_12}
-\exinput{exercises/03_01_ex_13}
-\exinput{exercises/03_01_ex_14}
+\exinput{exercises/03_01_ex_13}

exercises/03_03_ex_03.tex

@@ -1,4 +1,4 @@
-{Sketch a graph of a function on $[0,2]$ that is increasing but not strictly increasing.
+{Sketch a graph of a function on $[0,2]$ that is increasing, where it is increasing ``quickly'' near $x=0$ and increasing ``slowly'' near $x=2$.
 }
-{Answers will vary.
+{Answers will vary; graphs should be steeper near $x=0$ than near $x=2$.
 }

exercises/03_03_ex_26.tex

@@ -0,0 +1,4 @@
+{T/F: Functions always switch from increasing to decreasing, or decreasing to increasing, at critical points.
+}
+{False; for instance, $y=x^3$ is always increasing though it has a critical point at $x=0$.
+}

exercises/03_03_exercises.tex

@@ -3,6 +3,7 @@
 \exinput{exercises/03_03_ex_02}
 \exinput{exercises/03_03_ex_03}
 \exinput{exercises/03_03_ex_04}
+\exinput{exercises/03_03_ex_26}
 \exinput{exercises/03_03_ex_05}
 \printproblems
 \exsetinput{exercises/03_03_exset_01}

exercises/03_04_ex_55.tex

@@ -0,0 +1,6 @@
+{$\ds f(x) = \sec x $ on $(-3\pi/2,3\pi/2)$
+}
+{Possible points of inflection: $\fp'(x)$ is not defined (nor is $f$) at $x=-\pi/2,\pi/2$;
+concave down on $(-3\pi/2,-\pi/2)$ and $(\pi/2,3\pi/2)$
+concave up on $(-\pi/2,\pi/2)$
+}

exercises/03_04_ex_56.tex

@@ -0,0 +1,5 @@
+{$\ds f(x) = \sec x $ on $(-3\pi/2,3\pi/2)$
+}
+{max: at $x=\pm\pi$
+min: at $x=0$
+}

exercises/03_04_ex_57.tex

@@ -0,0 +1,4 @@
+{$\ds f(x) = \sec x $ on $(-3\pi/2,3\pi/2)$
+}
+{$\fp(x)$ has no relative extrema
+}

exercises/03_04_exset_01.tex

@@ -10,7 +10,6 @@
 \exinput{exercises/03_04_ex_07}
 \exinput{exercises/03_04_ex_08}
 \exinput{exercises/03_04_ex_09}
-\exinput{exercises/03_04_ex_10}
 \exinput{exercises/03_04_ex_11}
 \exinput{exercises/03_04_ex_12}
 \exinput{exercises/03_04_ex_13}

exercises/03_04_exset_02.tex

@@ -12,6 +12,7 @@
 \exinput{exercises/03_04_ex_20}
 \exinput{exercises/03_04_ex_21}
 \exinput{exercises/03_04_ex_22}
+\exinput{exercises/03_04_ex_55}
 \exinput{exercises/03_04_ex_23}
 \exinput{exercises/03_04_ex_24}
 \exinput{exercises/03_04_ex_25}

exercises/03_04_exset_03.tex

@@ -8,6 +8,7 @@
 \exinput{exercises/03_04_ex_33}
 \exinput{exercises/03_04_ex_34}
 \exinput{exercises/03_04_ex_35}
+\exinput{exercises/03_04_ex_56}
 \exinput{exercises/03_04_ex_36}
 \exinput{exercises/03_04_ex_37}
 \exinput{exercises/03_04_ex_38}

exercises/03_04_exset_04.tex

@@ -8,6 +8,7 @@
 \exinput{exercises/03_04_ex_46}
 \exinput{exercises/03_04_ex_47}
 \exinput{exercises/03_04_ex_48}
+\exinput{exercises/03_04_ex_57}
 \exinput{exercises/03_04_ex_49}
 \exinput{exercises/03_04_ex_50}
 \exinput{exercises/03_04_ex_51}

exercises/03_05_ex_30.tex

@@ -0,0 +1,4 @@
+{T/F: When sketching graphs of functions, one need not plot any points at all.
+}
+{F
+}

exercises/03_05_ex_31.tex

@@ -0,0 +1,5 @@
+{$\ds f(x) = ax^2+bx+1$
+}
+{Critical point: $x=-b/(2a)$
+No points of inflection
+}

exercises/03_05_exercises.tex

@@ -4,6 +4,7 @@
 \exinput{exercises/03_05_ex_03}
 \exinput{exercises/03_05_ex_04}
 \exinput{exercises/03_05_ex_05}
+\exinput{exercises/03_05_ex_30}
 \printproblems
 \exsetinput{exercises/03_05_exset_01}
 \exsetinput{exercises/03_05_exset_02}

exercises/03_05_exset_03.tex

@@ -2,5 +2,6 @@
 {, a function with the parameters $a$ and $b$ are given. Describe the critical points and possible points of inflection of $f$ in terms of $a$ and $b$.
 }
 \exinput{exercises/03_05_ex_26}
+\exinput{exercises/03_05_ex_31}
 \exinput{exercises/03_05_ex_27}
 \exinput{exercises/03_05_ex_28}

exercises/04_01_ex_19.tex

@@ -0,0 +1,4 @@
+{$f(x) = x^3-x^2+x-1$, $x_0=1$
+}
+{$x_0=1$, $x_1=1$, $x_2=1$, $x_3=1$, $x_4=1$, $x_5=1$
+}

exercises/04_01_exset_01.tex

@@ -6,3 +6,4 @@
 \exinput{exercises/04_01_ex_05}
 \exinput{exercises/04_01_ex_06}
 \exinput{exercises/04_01_ex_07}
+\exinput{exercises/04_01_ex_19}

exercises/04_04_ex_39.tex

@@ -0,0 +1,5 @@
+{T/F: In real life, differentials are used to approximate function values when the function itself is not known.
+}
+{T
+}
+

exercises/04_04_ex_40.tex

@@ -0,0 +1,5 @@
+{$f(x) = \ln\big(\sec x\big)$
+}
+{$dy = \big(\tan x\big)dx$
+}
+

exercises/04_04_exercises.tex

@@ -4,13 +4,11 @@
 \exinput{exercises/04_04_ex_03}
 \exinput{exercises/04_04_ex_04}
 \exinput{exercises/04_04_ex_05}
+\exinput{exercises/04_04_ex_39}
 \printproblems
 \exsetinput{exercises/04_04_exset_01}
 \exsetinput{exercises/04_04_exset_02}
-\exinput{exercises/04_04_ex_30}
-\exinput{exercises/04_04_ex_31}
-\exinput{exercises/04_04_ex_32}
-\exinput{exercises/04_04_ex_33}
+\exsetinput{exercises/04_04_exset_04}
 \exsetinput{exercises/04_04_exset_03}
 %\printreview
 %\exinput{exercises/03_03_ex_24}

exercises/04_04_exset_01.tex

@@ -1,5 +1,7 @@
 {\noindent In Exercises}
-{, use differentials to approximate the given value by hand.}
+{, use differentials to approximate the given value by hand.%
+%Used to have \exinput{exercises/04_04_ex_15} but took it out to get an even # of problems
+}
 \exinput{exercises/04_04_ex_06}
 \exinput{exercises/04_04_ex_07}
 \exinput{exercises/04_04_ex_08}
@@ -9,6 +11,4 @@
 \exinput{exercises/04_04_ex_12}
 \exinput{exercises/04_04_ex_13}
 \exinput{exercises/04_04_ex_14}
-\exinput{exercises/04_04_ex_15}
-\exinput{exercises/04_04_ex_16}
-
+\exinput{exercises/04_04_ex_16}

exercises/04_04_exset_02.tex

@@ -12,4 +12,5 @@
 \exinput{exercises/04_04_ex_26}
 \exinput{exercises/04_04_ex_27}
 \exinput{exercises/04_04_ex_28}
-\exinput{exercises/04_04_ex_29}
+\exinput{exercises/04_04_ex_29}
+\exinput{exercises/04_04_ex_40}

exercises/04_04_exset_04.tex

@@ -0,0 +1,7 @@
+{\noindent Exercises}
+{ use differentials to approximate propagated error.
+}
+\exinput{exercises/04_04_ex_30}
+\exinput{exercises/04_04_ex_31}
+\exinput{exercises/04_04_ex_32}
+\exinput{exercises/04_04_ex_33}

exercises/05_01_ex_42.tex

@@ -0,0 +1,5 @@
+{If $F(x)$ is an antiderivative of $f(x)$, and $G(x)$ is an antiderivative of $g(x)$, give an antiderivative of $f(x)+g(x)$.
+}
+{$F(x)+G(x)$
+}
+

exercises/05_01_exercises.tex

@@ -6,6 +6,7 @@
 \exinput{exercises/05_01_ex_05}
 \exinput{exercises/05_01_ex_06}
 \exinput{exercises/05_01_ex_07}
+\exinput{exercises/05_01_ex_42}
 \printproblems
 \exsetinput{exercises/05_01_exset_01}
 \exinput{exercises/05_01_ex_39}

exercises/05_02_ex_09.tex

@@ -13,7 +13,8 @@
 \item		$\ds \int_0^4 f(x)\ dx$
 \item		$\ds \int_0^4 5f(x)\ dx$
 \end{enumerate}
-\end{minipage}
+\end{minipage}%
+\ifthenelse{\boolean{printquestions}}{\columnbreak}{}
 }
 {\begin{enumerate}
 \item		$\pi$

exercises/05_02_ex_11.tex

@@ -14,6 +14,7 @@
 \item		$\ds \int_0^1 f(x)\ dx$
 \end{enumerate}
 \end{minipage}
+\ifthenelse{\boolean{printquestions}}{\vskip1in\ \columnbreak}{}
 }
 {\begin{enumerate}
 \item		$4/\pi$

exercises/05_02_ex_12.tex

@@ -14,7 +14,6 @@
 \item		$\ds \int_0^1 f(x)\ dx$
 \end{enumerate}
 \end{minipage}
-\ifthenelse{\boolean{printquestions}}{\vskip1in\ \columnbreak}{}
 }
 {\begin{enumerate}
 \item		$4$

exercises/05_02_ex_30.tex

@@ -0,0 +1,27 @@
+{\noindent
+\begin{minipage}{\linewidth}
+\myincludegraphics[scale=.8]{figures/fig05_02_ex_30}
+\end{minipage}
+\noindent\begin{minipage}[t]{.5\linewidth}
+\begin{enumerate}
+\item		$\ds \int_0^5 f(x)\ dx$
+\item		$\ds \int_3^7 f(x)\ dx$
+\end{enumerate}
+\end{minipage}
+\begin{minipage}[t]{.5\linewidth}
+\begin{enumerate}\addtocounter{enumii}{2}
+\item		$\ds \int_0^0 f(x)\ dx$
+\item		$\ds \int_a^b f(x)\ dx$, where 
+
+$0\leq a\leq b\leq 10$
+\end{enumerate}
+\end{minipage}
+}
+{\begin{enumerate}
+\item		$15$
+\item		$12$
+\item		$0$
+\item		$3(b-a)$
+\end{enumerate}
+}
+

exercises/05_02_exercises.tex

@@ -5,11 +5,11 @@
 \exinput{exercises/05_02_ex_04}
 \printproblems
 \exsetinput{exercises/05_02_exset_01}
-\ifthenelse{\boolean{printquestions}}{\columnbreak}{}
+%\ifthenelse{\boolean{printquestions}}{\columnbreak}{}
 \exsetinput{exercises/05_02_exset_02}
 \exsetinput{exercises/05_02_exset_03}
 \exinput{exercises/05_02_ex_16}
-\ifthenelse{\boolean{printquestions}}{\columnbreak}{}
+%\ifthenelse{\boolean{printquestions}}{\columnbreak}{}
 \exinput{exercises/05_02_ex_17}
 \exsetinput{exercises/05_02_exset_04}
 \ifthenelse{\boolean{printquestions}}{\columnbreak}{}