\magnification=\magstep1
\centerline{Mathematics 131 -- Calculus for Physical and Life Sciences 1}
\centerline{Exam 3 -- Things to Know}
\centerline{November 22, 2004}

\bigskip\noindent
{\it General Information}

\bigskip
\item{$\bullet$}
The third exam of the semester will be given 
on Wednesday evening, December 1 at 6:00pm, in Haberlin 103
(the large lecture hall on 1st floor Haberlin).  You will have
until 7:30pm to work on the exam if you need that much time.
\item{$\bullet$} Alternate time for those who have conflicts:
Wednesday evening, December 1,  7:30pm - 9:00pm.  If neither time works 
for you, contact me as soon as possible to arrange for another
time to take the exam.
\item{$\bullet$}
This exam will cover the material we have studied
since the second exam -- Sections 6-10 in Chapter 3, and sections
1,2,5 in Chapter 4 in the text.  (See below for a more
detailed breakdown of the topics to know.)  
\item{$\bullet$} A
basic scientific (non-graphing) calculator will be
provided for your use on the exam.  
\item{$\bullet$} You will not be allowed to use
cell-phones, computers, or any other electronic
devices during the exam.  Please do not bring them
with you; they will be subject to confiscation for
the period of the exam if you use them.

\bigskip\noindent
We will review for the 
exam in class on Tuesday, November 30.  

\bigskip\noindent
{\it Material To Know}

\bigskip\noindent
You should know the following topics (in addition
to basic derivative rules from earlier in the semester, of course!):

\bigskip\noindent
A)  Section 3.6: The method of deriving derivative
formulas for inverse functions using the chain rule.
Also derivatives of $\ln(u), \log_a(u), \arcsin(u), \arctan(u)$.
Related rates.
\bigskip\noindent
B)  Section 3.7: Implicit differentiation.  Know how to
differentiate implicitly given $f(x,y)$, also how to get
tangent lines to implicitly defined curves.  
\bigskip
\noindent
C) Section 3.8: Parametric curves.  Know the basic idea of describing
motion in the plane via parametric equations, how to combine graphs
of $x(t)$ and $y(t)$ versus $t$ to sketch a parametric curve, how
to compute speeds and slopes, also know the ``standard'' parametrizations
for lines, circles, ellipses, and how to use them.
\bigskip
\noindent
D)  Section 3.9: Know how to use the linear function defining
the tangent line to a graph $y = f(x)$ at $x = a$ to approximate
values of $f$ near $x = a$.
\bigskip\noindent
E)  Section 3.10:  Know how to use L'Hopital's Rule to evaluate
limits of ``$0/0$'' and ``$\infty/\infty$'' indeterminate forms.
Also know how to use L'Hopital to compare rates of growth of 
functions as $x\to \infty$.
\bigskip
\noindent
F)  Section 4.1: Know: The language of critical points, local maxima and
minimal, inflection points; How to find these using the first and
second derivatives; The first and second derivative tests for
critical points.  
\bigskip
\noindent
G)  Section 4.2: Finding critical points, etc. in families of 
curves.
\bigskip
\noindent
H)  Section 4.3:  Optimization for $f(x)$ on closed intervals --
know how to find local maxima and minima as in 4.1 above, then
compare the function values at those points with values at the 
endpoints to find the overall maximum and minimum on an interval.
\bigskip
\noindent
I)  Section 4.5:  Applied optimization story problems.  Know
how to set up and solve questions like ones from Problem Set 11.
\bigskip\noindent
{\it Some Good Review Problems}

\bigskip\noindent
\bigskip
\noindent
Section 3.8/3, 11, 13, 15, 27, 31 (what $xy$ equation is satisfied by all of these?)
\bigskip
\noindent
Section 3.10/5, 7, 9, 11
\bigskip\noindent
From the Review problems at the end of Chapter 3: All the problems
1-52 should be functions you can differentiate now.  To keep your
skills sharp, pick a ``representative sample'', 55, 57, 77, 
\bigskip\noindent
Section 4.5/5, 6, 7, 8, 15, 21
\bigskip\noindent
From the Review problems at the end of Chapter 4: 
1, 3, 5, 7, 9, 23, 24, 27

\bigskip\noindent
The ``Check Your Understanding Problems'' at the end of Chapter 3 and Chapter 4
are also very good for studying.
\bye
