Information for Second Midterm Exam Math 1b Fall '99
Well, it's all done now. Here are the solutions to the second midterm:
Solutions
for Exam 2, Fall 99
Old info:
On the second midterm you should be prepared to answer
questions from any of the following topics:
Note - this second test just covers the material on
integration from the second part of the semester - it will not include
infinite series topics.
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Integration techniques:
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integration by substitution
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integration by parts - be able to handle "trick" integrals
like ln x, and other interesting by parts integrals
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partial fractions (just need to know how to handle non-repeated
linear factors, no quadratic irreducibles)
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improper integrals - know how to recognize and evaluate them
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Integration applications:
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volume integrals - volumes of rotation, volumes given with
specified cross-section areas, intersections of objects, etc.
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note you just need to know how to compute volumes using disks/washers
approach, not shells method
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arc length computations - know the formula!
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note you don't need to know how to deal with the arc length
formula for parametrized curves (formula 8.4.3)
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surface area computations - know the formula!
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work integrals - know how to set up expressions involving
force and how to compute work by evaluating definite integrals
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note the purpose of the exam questions is to test your understanding
of the math concepts, not the physics concepts, so don't worry about whether
or not you have a physics background. Do be sure to review the homework
problems from section 8.6 carefully so that you understand the basic situations
covered in those problems.
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Fluid pressure - again, know how to calculate fluid pressure
by setting up and evaluating appropriate definite integrals
Old Exams for practice:
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We will post solutions to these two exams shortly... first try to do them
on your own!
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our exam should be quite similar in length and topic coverage as compared
to these two exams (i.e. if you can't do any of these problems then you
need to start studying!)
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Exam
2, Fall 98
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Note: problem 4 is very difficult to solve as stated unless you know
an extra trick which we didn't cover this semester. Try the same
problem but treat it as a surface of revolution around the x-axis instead
of around the y-axis (the answer to this modified problem is in the solution
set below).
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(Solutions
for Exam 2, Fall 98)
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Exam
2, Spring 99
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(Solutions
for Exam 2, Spring 99)
Useful Reference Handouts:
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Here are two review worksheets which provide more practice problems for
each of the topics on the exam
(you can find the solutions to the example problems worked out at the
end of each handout)
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your T.F. might work through these review worksheets in your class, so
you might want to check with them before you do the worksheets on your
own.