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\centerline{Mathematics 131 -- Calculus for Physical and Life Sciences 1}
\centerline{Exam 2 -- Things to Know}
\centerline{October 19, 2004}

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{\it General Information}

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\item{$\bullet$}
The second exam of the semester will be given 
on Wednesday evening, October 27 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, October 27,  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 first exam -- Chapter 2 and sections 1 - 5
of Chapter 3 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.

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We will review for the 
exam in class on Tuesday, October 26.  

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{\it Material To Know}

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You should know the following topics:

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A)  Section 2.1 -- Average velocity
($v_{ave} = {x(t+\Delta t) - x(t) \over \Delta t}$)
and instantaneous velocity 
($v_{inst} = \lim_{\Delta t \to 0} {x(t+\Delta t) - x(t) \over \Delta t}$).
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B)  Section 2.2 -- Limits
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\item{1)}  Know the precise definition of the statement
$\lim_{x \to c} f(x) = L$ (see page 64 in text or class notes) and
what it means 
\item{2)} Know the Limit Theorems (Theorem 2.1 in text) and 
how to use them to evaluate limits.
\item{3)} Know how to tell when $\lim_{x\to c} f(x)$ does not exist
because one-sided limits are different or because $f(x)$ has an
infinite discontinuity at $c$. 
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\noindent
C) Section 2.3 -- The Derivative at a point
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\item{1)}  Know the precise definition 
$f'(x) = \lim_{h\to 0} {f(x + h) - f(x) \over h}$ 
(limit of the difference quotient for $f$) and how
to apply it to compute some simple derivatives (like ones from
problem sets and class notes)
\item{2)}  Also know how to estimate $f'(x)$ numerically 
by approximating the limit of the difference quotient.
\item{2)}  Know the interpretation of $f'(x)$ as the slope
of the tangent line to $y = f(x)$ at $x$, and how to find the
equation of the tangent line at a given point.
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\noindent
D)  Section 2.4 -- The Derivative function 
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\item{1)}  Know how to sketch a qualitative graph of $y = f'(x)$,
given the graph $y = f(x)$ without $y$-axis scale 
\item{2)}  Also know how to estimate $f'(x)$,
given the graph $y = f(x)$ with coordinate grid. 
\item{3)}  $f'$ positive on an interval implies $f$ is increasing
on that interval; $f'$ negative on an interval implies $f$ is decreasing
on that interval
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E)  Section 2.5 -- Interpretations of the derivative
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\item{1)}  Know how to interpret the derivative as the instantaneous
rate of change of the function, and how to determine units for
the derivative
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F)  Section 2.6 -- The second derivative
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\item{1)} $f''$ positive on an interval implies $f'$ is increasing
on that interval and graph of $f$ is concave up; 
$f''$ negative on an interval implies $f'$ is decreasing
on that interval and graph of $f$ is concave down
\item{2)} second derivative of position with respect to time is 
acceleration
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\noindent
G)  Section 2.7 -- Continuity and differentiability
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\item{1)}  Precise definition of continuity:  $f$ is continuous
at $x = c$ if $\lim_{x \to c} f(x) = f(c)$.
\item{2)}  Know that sharp corners, cusps, or vertical tangents give
points where a function is not differentiable
\item{3)}  If $f$ is differentiable at $x$, then $f$ is continuous at $x$. 
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\noindent
H)  Sections 3.1 and 3.2 -- Derivative rules for sums, constant multiples,
powers, polynomials, exponentials (Know how to apply all of these on
functions like ones seen on problem sets, etc.)
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\noindent
I)  Section 3.3 -- Product and Quotient Rules -- know the statements 
and how to apply them
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J)  Section 3.4 -- Chain Rule -- know the statement
and how to apply it
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K) Section 3.5 -- Derivatives of trigonometric functions
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{\it Some Good Review Problems}

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From the Review problems at the end of Chapter 2:  1-8, 13-15, 22, 25, 28,
29, 31, 36
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From the Review problems at the end of Chapter 3: All the problems
1-52 except ones involving $\arcsin$, $\arctan$ are good practice -- 
you don't need to do them all, but pick a ``representative sample'', 
60, 69, 70, 72

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The ``Check Your Understanding Problems'' at the end of Chapter 2 and Chapter 3
are also very good for studying.
\bye
