Section 18.5: Review for Chapter 18

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.

Here are the new terms in Chapter 18.

Antiderivative [18.4]
Area function [18.4]
Area under a curve [18.4]
Average rate of change [18.3]
Calculus [18.1]
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]
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]
Tangent line formula [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 ex [18.3]
Area function [18.4]
Antiderivative [18.4]
Antiderivative of ex [18.4]

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]
Guess the limit of a sequence. [18.1]
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 text 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.