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Studying for a chapter examination is
a personal process, one which nobody else can do for you.
Simply take the time to review what you have done.
Antiderivative [18.4]
Antiderivative of a sum [18.4]
Antiderivative of e^x [18.4]
Area function [18.4]
Area under a curve [18.4]
Average rate of change [18.3]
Calculus [18.1]
Constant multiple [18.4]
Converge [18.2]
Definite integral [18.4]
Derivative [18.1; 18.3]
Differentiable function [18.3]
Differential calculus [18.1]
Diverge [18.2]
Dummy variable [18.4]
General term [18.2]
Indefinite integral [18.4]
Instantaneous rate of change [18.3]
Integral [18.1]
Integral calculus [18.1]
Integral of a sum [18.4]
Integrand [18.4]
Limit [18.1]
Limit of a sequence [18.2]
Limits of integration [18.4]
Mathematical modeling [18.1]
Predecessor [18.2]
Secant line [18.1]
Sequence [18.2]
Successor [18.2]
Tangent line [18.1, 18.3]
Velocity [18.3]
If you can describe the term, read on to the next one;
if you cannot, then look it up in the text (the section
number is shown in brackets).
Can you explain each of these important ideas in your
own words?
Nature of calculus [18.1]
Mathematical modeling [18.1]
Limit of a sequence [18.2]
Limits to infinity [18.2]
Derivative [18.3]
Derivative of e^x [18.3]
Area function [18.4]
Antiderivative [18.4]
Antiderivative of e^x [1.8]
Next, make sure you understand the types of problems
in Chapter 18.
Describe the limit process, including Zeno's paradox.
[18.1]
Describe the derivative, including the tangent problem.
[18.1]
Describe the integral, including the area problem. [18.1]
Be able to guess the limit of a sequence. [18.1]
Be able to draw the line tangent to a curve at a specified
point. [18.1]
Approximate an area by using rectangles. [18.1]
Explain the process of mathematical modeling. [18.1]
Write out the first 5 terms of a sequence when given a general
term. [18.2] Find the limit of a sequence. [18.2]
Solve applied problems involving limits of sequences. [18.2]
Estimate a rate of change by looking at a graph. [18.3]
Estimate the slope of a tangent line by looking at a graph.
[18.3]
Find an average rate of change for a given function over
an interval. [18.3]
Find an instantaneous rate of change for a given function
at a particular point. [18.3]
Find the derivative by using the definition of derivative.
[18.3]
Find the equation of a tangent line. [18.3]
Evaluate an area function. [18.4]
Find an antiderivative. [18.4]
Find the area under a curve. [18.4]
Approximate the value of a definite integral by using areas.
[18.4]
Once again, see if you can verbalize (to yourself) how
to do each of the listed types of problems. Work all of
Chapter 18 Review Questions (whether they are assigned
or not).
Work through all of the problems before looking at the
answers, and then correct each of the problems. The entire
solution is shown in the answer section at the back of the
text. If you worked the problem correctly, move on to the
next problem, but if you did not work it correctly (or you
did not know what to do), look back in the chapter to study
the procedure, or ask your instructor. Finally, go back
over the homework problems you have been assigned. If you
worked a problem correctly, move on the next problem, but
if you missed it on your homework, then you should look
back in the book or talk to your instructor about how to
work the problem. If you follow these steps, you should
be successful with your review of this chapter.
We give all of the answers to the Chapter Review questions
(not just the odd-numbered questions), so be sure to check
your work with the answers as you prepare for an examination.
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