Guidelines in reviewing for Exam 3
Exam 3 is cumulative, but will focus upon class material in
Sections 3.10, 4.1-4.8, and 5.1-5.3.
Following is a list amassing together the daily goals for days
covering material in the sections listed above. In studying for
this exam, you are of course encouraged to look over class notes
and examples, homework (don't just look over your past write-ups;
try to re-work a smattering of assigned problems from
scratch) and problems from the Practice Exercises
sections at the ends of chapters. You should also assess your
readiness for the exam based on the list of goals.
Goals for Class Date: Oct. 12, 2007
Students should be able to
- state sufficient conditions under which a function
has an absolute maximum and minumum.
- state what the term critical point of f
means in general, and find any/all such points for
various f.
- state what is meant by the terms absolute maximum
and absolute minumum, and use calculus to find
absolute extrema for various f.
Goals for Class Date: October 16, 2007
Students should be able to
- give a complete statement of the Mean Value Theorem,
along with the special case known as Rolle's Theorem.
- understand what the Mean Value Theorem is saying,
both graphically, and in terms of average vs. instantaneous
rates of change.
- identify situations in which the hypotheses of the
Mean Value Theorem are in place, and use it to answer
questions in those situations.
Goals for Class Date: October 17, 2007
Students should be able to
- understand the relationship between the sign of a function's
derivative and its increasing/decreasing behavior, as expressed
in Corollary 3, p. 254.
- apply the first derivative test (found in the box on p. 256)
to find local extrema.
Goals for Class Date: Oct. 22, 2007
Students should be able to
- explain how the sign of the 2nd derivative of a function
is related to the increasing/decreasing nature of the
1st derivative, as well as the concavity of the function.
- use calculus to locate points of inflection.
- use the 2nd derivative test to identify if a critical
point of f corresponds to a local extremum, or
say why the 2nd derivative test does not work.
Goals for Class Date: Oct. 25, 2007
Students should be able to
- take a verbal description of the problem and identify
appropriate dependent and independent variables.
- write a function, identifying and using one or more
auxilliary equations as needed, giving the dependent
variable in terms of the independent variable.
- identify an appropriate domain for the function mentioned
above.
- find, as desired, minima or maxima of the function
over the appropriate domain.
Goals for Class Date: Oct. 29, 2007
Students should be able to
- identify situations in which L'Hôpital's
rule is applicable.
- apply L'Hôpital's rule in conjunction with
other limit rules (from Chapter 2) in order to
evaluate limits.
Goals for Class Date: Oct. 30, 2007
Students should be able to
- identify limit forms which are and are not indeterminate.
- apply appropriate algebraic techniques to deal with
various indeterminate forms which cannot initially
be handled using L'Hôpital's Rule.
Goals for Class Date: Oct. 31, 2007
Students should be able to
- find the linearization of a differentiable function
f about a point x = a, and use it to
find approximate values of f(x) for
x-values close to x = a.
- take problems which involve solving an equation and
recast them as problems for finding the zeros of a
function.
- describe visually just what Newton's Method does
in order to find a zero of a function. This also
entails being able to demonstrate why Newton's
Method sometimes fails to find a zero.
- use Newton's Method to find approximate zeros of
a function.
Goals for Class Date: Nov. 5, 2007
Students should be able to
- check whether one function is an antiderivative of
another.
- describe the meaning of the indefinite integral
of f.
- find antiderivatives of various given functions.
- identify various properties (sum and differences,
constant multiples) of the indefinite integral.
Goals for Class Date: Nov. 6, 2007
Students should be able to
- set up an approximating sum of areas of rectangles for the
area under a curve using whatever rule desired: an
upper sum, a lower sum, a left or right-hand sum, or a midpoint
rule. After doing so, they should be able to calculate the
resulting value.
- set up rectangle sums in the same way as above when
the function is a rate of change of something, and use
them to approximate the total change of that thing.
- find the exact area under a non-negative function when
that function is piecewise linear.
Goals for Class Date: Nov. 7, 2007
Students should be able to
- turn a sum expressed involving sigma notation into one
where the individual summands all appear.
- take various sums and rewrite them in sigma notation.
Goals for Class Date: Nov. 9, 2007
Students should be able to
- state what is required for a definite integral of f
from a to b to exist.
- state and use the properties of the definite integral.
- explain what the definite integral tells us in terms of
areas of regions lying between the integrand (function)
and the x-axis.
- evaluate the definite integral when the integrand produces
regions involving simple geometric shapes (circles, rectangles
and triangles).
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