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\centerline{Mathematics 134 -- Intensive Calculus for Science 2}
\centerline{Exam 1 -- Things To Know}
\centerline{February 12, 2000}
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{\it General Information}
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As announced in the course syllabus, the first full-period
midterm exam of the semester will be given in class on Friday, 
February 16.  The format will be similar to that of the midterm exams
last semester.  The exam will cover the material since the start
of the semester (Quizzes 1,2,3), including the following material from 
Chapter 3 sections 4, Chapter 6 sections 1,2,3, and 
Chapter 7 sections 1,2,3,4 of the text:
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\item{1)}  The Fundamental Theorem of Calculus:  If $F(x)$
is an antiderivative of a continuous function $f(x)$ on $[a,b]$, then 
$$\int_a^b f(x)\ dx = F(b) - F(a)$$
\item{2)}  Antiderivatives graphically and numerically
\item{3)}  The power, sum, and constant multiple rules for antiderivatives
\item{4)}  Differential equations ${dy\over dx} = f(x)$
\item{5)}  Indefinite integrals by substitution
\item{6)}  Integration by parts
\item{7)}  Using the table of integrals
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\noindent
There will be a review for the exam in class on Thursday, February 15.  
I will also set up an evening session with Jodi Marani on Thursday for 
other questions.
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{\it Sample Exam}
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\noindent
I.  The following graph shows $y = F'(x)$, the {\it derivative}
of $F$.  Sketch the graphs $y = F(x)$ in the cases $F(0) = 0$ and $F(0) = 1$.
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\noindent
II.  A child throws a baseball vertically upward with velocity 12 ft/sec 
from an initial height of 4 feet.
The acceleration of the baseball due to gravity is -32 ft/sec${}^2$.
\item{A)} Make a table showing the velocity of the baseball
at 1/8 second intervals for $t = 0$ to $t = 1$.
\item{B)}  When does the baseball reach its highest point?  When
does it hit the ground?
\item{C)}  Find the greatest height the ball reaches.
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\noindent
III.  Compute the following integrals.  Say which method you 
are using for each.  If you use an entry from the table of 
integrals, say which one.
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\item{A)}  $\int 5x^4 - 3\sqrt{x} + e^x\ dx$
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\item{B)}  $\int x(4x^2 - 3)^{3/5}\ dx$
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\item{C)}  $\int_1^2 \sin^2(\pi x)\cos(\pi x)\ dx$
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\item{D)}  $\int x^2 e^{4x}\ dx$
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\item{E)}  $\int {dx\over \sqrt{1 - 9x^2}}$
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\item{F)}  $\int e^{3x}\cos(4x)\ dx$

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\noindent
Also see Problem Sets 1,2,3, the last three quizzes, and 
the Review Problems from the ends of Chapters 3,6,7 in
the text for other practice problems.
\bye
