Section 100 (Barsamian)

Quiz Study Guides

The quiz will be two problems, as follows:

Quiz Problem [1]: A problem similar to Suggested Exercises 2.1 # 47, 49

To prepare for Quiz Problem [1]

- Study Class Notes
- Read Section 2.1 pages 95 – 99
- Note that there are no book examples exactly like those suggested exercises. In order to prepare for solving those exercises, you should study Examples 3 and 4. Those examples start with a graph, and then they describe its limit behavior.
- Solve Matched problems 3 and 4.
- Solve Section 2.1 Exercises #47,49. These two exercises do the reverse of examples 3 and 4. That is, the exercises prescribe some limit behavior, and ask you to sketch a possible graph.

Quiz Problem [2] One problem similar to Suggested Exercises 2.1 # 61, 63:

To prepare for Quiz Problem [2]

- Study Class Notes
- Read Section 2.1 pages 100 - 105.
- Study Examples 8 and 9.
- Solve Matched problems 8 and 9.
- Solve Section 2.1 Exercises #61, 63

The quiz will be one problem involving infinit limits and vertical asymptotes, similar to one of these five suggested exercises from Section 2.2: # 19, 21, 35, 37, 39

This is material from Section 2.2 and involves an analytic approach to infinite and vertical asymptotes. *Some of this material may not have been covered in class.* This quiz is meant to test whether you have read the book, studied the examples, and worked on the Matched Problems and Suggested Exercises.

To prepare for the quiz

- Study Class Notes
- Read Section 2.2 pages 109 – 112, the sections titled
*Infinite Limits and Locating Vertical Asymptotes.* - Study Examples 1 and 2.
- Solve Matched Problems 1 and 2.
- Solve these five suggested exercises from Section 2.2: # 19, 21, 35, 37, 39

The quiz will be one problem involving limits at infinity and horizontal asymptotes, similar to one of these nine problems from Section 2.2: # 43, 47, 51, 53, 63, 65, 67, 69

This is material from Section 2.2 and involves an analytic approach to limits at infinity and horizontal asymptotes. Some of this material may not have been covered in class. This quiz is meant to test whether you have read the book, studied the examples, and worked on the Matched Problems and Suggested Exercises.

To prepare for the quiz

- Study Class Notes
- Read Section 2.2 pages 112 - 117.
- Study Examples 3, 4, 5, 6.
- Solve Matched Problems 3, 4, 5, 6.
- Solve Section 2.2 Suggested Exercises # 43, 47, 51, 53, 63, 65, 67, 69

The quiz will consist of one problem involving using a sign chart to solve an inequality, similar to one of these four suggested exercises from Section 2.3: # 47, 49, 51, 53

This is material from Section 2.3 and involves using a sign chart to solve an inequality. Some of this is material that we will start discussing in class *after* the quiz. This quiz problem is meant to test whether you have studied the book material that we are going to cover in class that day.

To Study for the quiz

- Read Section 2.3 pages 121 – 128
- Study Example 4 and the discussion that follows that example
- Solve Matched Problem 4
- Solve Suggested Exercises 2.3 # 47, 59, 51, 53

The quiz will be one problem that will be one of the following three types

- involving a difference quotient, similar to suggested exercise 2.4#9
- involving a secant line, similar to suggested exercises 2.4 # 43ab
- involving average velocity, similar to suggested exercises 2.4: # 13ab, 45ab

This is material from Section 2.4 that we will start discussing in class *after* the quiz. This quiz problem is meant to test whether you have studied the book material that we are going to cover in class that day.

To prepare for the quiz

- Read Section 2.4 pages 132 – 137.
- Study Examples 1,2,3
- Solve Matched Problems 1,2,3
- Solve Suggested Exercise 2.4 #9, 13ab, 43ab, 45ab

Quiz 6 will be two problems, as follows:

Given function *f *(*x*), use the *Definition of the Derivative* to find *f '*(*x*). The function *f *(*x*) will be a quadratic polynomial function, similar to Section 2.4 Example 4 and Suggested Exercise 2.4 # 27.

To prepare for the quiz

- Read Section 2.4 pages 138 – 142 material about The Derivative.
- Study Examples 4, 5
- Solve Matched Problems 4, 5
- Study Class Notes
- Solve Suggested Exercise 2.4 #27

**Remarks: **

- You must find
*f '*(*x*) using the*Definition of the Derivative*. That is, you must caluculate the limit given in the definition on page 138 of the textbook. Examples 4, 6, and 7 in the book show how such calculations are done. - You will be asked to show all calculations clearly, explain key steps, and use correct notation. In particular, you need to explain why you are allowed to cancel the
*h*/*h*term. This is one of the most important concepts of the course. Notice that the textbook reading and textbook examples do not really explain why that cancellation can be done. Pay attention in class, because we will be discussing that concept.)

The quiz will be five questions (A),(B),(C),(D),(E) of this format:

Given function *f *(*x*), find *f '*(*x*).

In each problem, function *f *(*x*) will be one of these types:

- a constant function, similar to Section 2.5 Example #1 or Suggested Exercise 2.5 # 9
- a power function, similar to Section 2.5 Example #2 or Suggested Exercises 2.5 # 11, 13, 15, 17
- a power function that is disguised using root notation and/or fraction notation, similar to Example #3 or Suggested Exercise 2.5 # 19, 53

This is material from Section 2.5 and involves using the *Constant Function Rule* or the *Power Rule* to find a derivative. That is material that we will start discussing in class *after* the quiz. This quiz problem is meant to test whether you have studied the book material that we are going to cover in class that day.

To Study for the quiz,

- Read Section 2.5 pages 147 – 149
- Study Examples 1,2,3
- Solve Matched Problems 1,2,3
- Solve Suggested Exercises 2.5 # 9, 11, 13, 15, 17, 19, 53

(Remark: In each question on this quiz, you should use the *Constant Function Rule* or the *Power Rule* to find *f '*(*x*). Do not use the *Definition of the Derivative*.)

Quiz 8 will be one problem of this format:

Given function *f *(*x*) involving a sum of fractions containing constants and powers of x.

(A) Rewrite *f *(*x*) as a sum of terms that are each made up of a constant times a power function.

(B) Find *f '*(*x*). (Use the *Sum* and *Constant Multiple Properties*, along with the *Power Rule* and the *Constant Function Rule*.)

(C) Simplify your answer. (Be sure to rewrite your answer, if necessary, so that it has no negative exponents.)

The function *f *(*x*) will be similar to the functions from Suggested Exercises 2.5 # 45, 49, 51, 53, 55, 81

This is material from Section 2.5 that involves using the *Sum* and *Constant Multiple Properties* to find a derivative. That is material that we will start discussing in class *after* the quiz. This quiz problem is meant to test whether you have studied the book material that we are going to cover in class that day.

To prepare for Quiz 8

- Read about the
*Constant Multiple Property*and the*Sum and Difference Property*in Section 2.5 on pages 150 - 152. - Study Section 2.5 Examples 4, 5, 6
- Solve Section 2.5 Matched Problems 4, 5, 6
- Solve Suggested Exercises 2.5 # 45, 49, 51, 53, 55, 81

(Remark: On this Quiz, you should find *f '*(*x*) using the *Sum* and *Constant Multiple Properties*, along with the *Power Rule* and the *Constant Function Rule*. Do not use the *Definition of the Derivative*.)

Quiz 9 will be two problems.

Problem [1] (5 points) will be similar to an Applications problem from Section 3.1. That is, it will be similar to one of the Suggested Exercises 3.1 # 25, 27, 29, 33, 35, 39, 41, 43.

To prepare for quiz problem [1]

- Read Section 3.1 on pages 181 - 184.
- Study Examples 1, 2, 3, 4
- Solve Matched Problems 1, 2, 3, 4
- Solve Suggested Exercises 3.1 # 25, 27, 29, 33, 35, 39, 41, 43

Problem [2] (5 points) will be five basic derivatives involving the derivatives of the natural exponential and natural logarithm functions. This is material from Section 3.2, which we will start discussing in class *after* the quiz. This quiz problem is meant to test whether you have studied the book material that we are going to cover in class that day.

To prepare for quiz problem [2]

- Read Section 3.2 pages 187 – 190, the material on the derivative of the
*natural exponential*and*natural logarithm*functions,*e*^{(x)}and ln(*x*). - Study Examples 1 and 2
- Solve Matched Problems 1 and 2
- Solve Suggested Exercises 3.2 # 9, 11, 17, 23

Quiz 10 will be one problem that will be one of the following two types:

- An exercise similar to one of the suggested exercises 3.2 # 47, 49, 51, 53 (Bases other than
*e*.) - An exercise similar to one of the suggested exercises 3.2 #63, 65, 67, 71 (Applications)

Some similar examples may have been discussed in class on Wednesday, September 23. But similar examples for some of the exercises will not be discussed in class until after Quiz 10 on Friday, September 25th, and some of the exercises will not be discusssed in class at all. This quiz problem is meant to test whether you have studied the book material that we are going to cover in class on Friday, September 25th and worked on solving exercises based on that material.

To prepare for quiz 10

- Read Section 3.2 from the bottom of page 190 through page 194 (The sections titled
*Other Logarithmic and Exponential Functions*and*Exponential and Logarithmic Models*). - Study Examples 3, 4, 5, 6
- Solve Matched Problems 3, 4, 5, 6
- Solve Suggested Exercises 3.2 # 47, 49, 51, 53, 63, 65, 67, 71

Quiz 11 will be one problem similar to one of the Suggested Exercises 3.3 # 17, 19, 21, 55. These exercises involve the derivative of a product or a derivative of a quotient. This is material from Section 3.3, which we will start discussing in class *after* the quiz. This quiz problem is meant to test whether you have studied the book material that we are going to cover in class that day.

To prepare for quiz 11

- Read Section 3.3, pages 196 – top of page 198, on the derivatives of products
- Study Examples 1 and 3
- Solve Matched Problems 1 and 3
- Solve Suggested Exercises 3.3 # 17, 19, 21, 55

Quiz 12 will be one moderately difficult problem involving the quotient rule. It will be based on one of the suggested exercises 3.3 # 25, 31, 33, 59, 73, 87

To prepare for Quiz 12

- Read Section 3.3, pages 198 - 201, on the derivatives of quotients
- Study Examples 4, 5, 6
- Solve Matched Problems 4, 5, 6
- Solve Suggested Exercises 3.3 # 25, 31, 33, 59, 73, 87
- Study Class Notes
- Study Class Drill 10

Quiz 13 will be two problems similar to Suggested Exercises 3.4 # 21, 29, 31, 37, 59. These exercises involve the derivative of a composite function where the outer function is a power function. The derivatives are found using the *General Power Rule*. This is material from Section 3.4, which we will start discussing in class *after* the quiz. This quiz problem is meant to test whether you have studied the book material that we are going to cover in class that day.

To prepare for Quiz 13

- Read Section 3.4, pages 204 – top of page 208, on the
*General Power Rule* - Study Examples 1, 2, 3
- Solve Matched Problems 1, 2, 3
- Solve Suggested Exercises 3.4 # 21, 29, 31, 37, 59

Quiz 14 will be one problem of one of the following types

- Either an (A),(B),(C),(D),(E) problem similar to suggested exercises 4.1 # 9, 10, 11, 12, 13, 14
- Or a problem similar to one of the suggested exercises 4.1 # 53, 55, 57

These exercises are about the relationship between the increasing/decreasing behavior of a function *f *(*x*) and the sign of the derivative *f ' *(*x*). This is material from Section 4.1, which we will start discussing in class *after* the quiz. This quiz problem is meant to test whether you have studied the book material that we are going to cover in class that day.

To prepare for Quiz 14

- Read Section 4.1, pages 238 - 239
- Study Example 1
- Solve Matched Problem 1
- Solve Suggested Exercises 4.1 # 53, 55, 57

Quiz 15 will be one problem about these topics

- partition numbers for
*f '*and critical numbers for*f* - local extrema of
*f* - The First Derivative Test

The quiz problem will be based on one of these suggested exercises: 4.1 # 17, 19, 21, 23, 25, 27, 41

To prepare for Quiz 15

- Read Section 4.1, pages 240 - 246
- Study Examples 2, 6, 7
- Solve Matched Problems 2, 6, 7
- Study Class Notes
- Study Class Drills 15, 16
- Solve Suggested Exercises 4.1 # 17, 19, 21, 23, 25, 27, 41

Quiz 16 will be one problem about these topics

- partition numbers for
*f '*and critical numbers for*f* - increasing & decreasing behavior of
*f* - local extrema of
*f*

The quiz problem will be based on one of these suggested exercises: 4.1 # 29, 31, 41, 43, 85, 97

To prepare for Quiz 16

- Read Section 4.1, pages 238 - 246
- Study Examples 3,4,5
- Solve Matched Problems 3,4,5
- Study Class Notes
- Solve Suggested Exercises 4.1 # 29, 31, 41, 43, 85, 97

Quiz 17 will be one problem. Given a formula for a function *f* , you will answer questions about

- the second derivative of
*f* - concavity behavior of
*f* - inflection points of
*f*

The quiz problem will be based on one of these suggested exercises: 4.2 # 17, 19, 33, 35, 37

This is material that we will start discussing in class *after* the quiz. This quiz problem is meant to test whether you have studied the book material that we are going to cover in class that day.

To prepare for Quiz 17

- Read Section 4.2, pages 254 – middle of 260
- Study Examples 1, 2, 3
- Solve Matched Problems 1, 2, 3
- Solve Suggested Exercises 4.2 # 17, 19, 33, 35, 37

Quiz 18 will be one problem about the *Closed Interval Method*:

Given a function *f *(*x*) and a closed interval [a,b], use the *Closed Interval Method* to find the absolute maximum and absolute minimum values of *f *(*x*) on the interval [a,b].

(You must use calculus and show all details clearly. No credit for just guessing *x*-values.)

The quiz problem will be based on one of these suggested exercises: 4.5 # 26, 67

This is material that we will start discussing in class *after* the quiz. This quiz problem is meant to test whether you have studied the book material that we are going to cover in class that day.

To prepare for Quiz 18

- Read Section 4.5, pages 293 – top of 296
- Study Example 1
- Solve Matched Problem 1
- Solve Suggested Exercises 4.5 # 26, 67

Note that the *Closed Interval Method* involves the following:

- finding critical numbers for the function
*f*. This must be done using calculus. - making a list of important
*x*-values where the absolute max & min can occur. This list of*x*-values consists of the endpoints of the interval and any critical numbers that are in the interval. (Note that you will get no credit for just making a list of all the integer*x*-values in the interval and computing the corresponding*y*-values. You must use calculus and find the critical numbers, and your list of important*x*-values should just be the endpoints of the interval and the critical numbers in the interval.) - Computing the corresponding
*y*-values of*f*at each of the important*x*-values on the list. - Identifying the greatest and least
*y*-values as the absolute max and absolute min.

Quiz 19 will be one problem about the *Second Derivative Test for Local Extrema* or the *Second Derivative Test for Absolute Extrema on an Open Interval*.

The quiz problem will be based on Section 4.5 Example 2 or Example 3.

This is material that we will start discussing in class *after* the quiz. This quiz problem is meant to test whether you have studied the book material that we are going to cover in class that day.

To prepare for Quiz 19

- Read Section 4.2, Middle of 296 - 299
- Study Examples 2 and 3
- Solve Matched Problems 2 and 3

Quiz 20 will be one problem about Maximizing Area or Minimizing Cost.

The quiz problem will be based on Section 4.6 Examples # 1,2 or Suggested Exercises 4.6 # 33, 34.

*after* the quiz. This quiz problem is meant to test whether you have studied the book material that we are going to cover in class that day.

To prepare for Quiz 20

- Read Section 4.6, page 301 – middle of 304 (the material titled
*Area and Perimeter*) - Study Examples 1 and 2
- Solve Matched Problems 1 and 2
- Solve Suggested Exercise 4.6 # 33, 34

Quiz 21 will be one A,B,C,D,E problem about antiderivative. Each of the A,B,C,D,E parts will be of this type:

Given some functions *f* and *g*, determine whether or not *f* is an antiderivative of *g*.

The quiz problem will be based on Section 5.1 Suggested Exercises 5.1 # 25, 27, 29, 31, 33, 34, 35, 36, 37, 38

*after* the quiz. This quiz problem is meant to test whether you have studied the book material that we are going to cover in class that day.

To prepare for Quiz 21

- Read Section 5.1, page 320 – middle of 321 (the material titled
*Antiderivatives*) (Note the observations provided below.) - Study Example 1
- Solve Matched Problem 1
- Solve Suggested Exercise 5.1 # 25, 27, 29, 31, 33, 34, 35, 36, 37, 38

Observations about the reading: This section introduces a new word, *antiderivative*. Here is a definition:

**Definition of antiderivative**

**words:***f*is an antiderivative of*g*.**meaning:***g*is the derivative of*f*.**meaning, in symbols:***f ' = g*.

Given some functions * f * and *g*, suppose you want to determine whether or not * f * is an antiderivative of *g*. Simply find * f '*.

- If
*f '*matches*g*, then*f*is an antiderivative of*g*. - If
*f '*does not match*g*, then*f*is not an antiderivative of*g*.

In other words, the only math that you need to do on this quiz will be derivatives. That is old math. But the questions will be written using the new word, antiderivatives.

Quiz 22 will be two problems involving indefinite integrals.

The problems will be based on Section 5.1 Suggested Exercises 5.1 # 43, 45, 47, 49, 51, 53

Some of this is material that we will start discussing in class *after* the quiz. This quiz problem is meant to test whether you have studied the book material that we are going to cover in class that day.

To prepare for Quiz 22

- Read Section 5.1, middle of 321 – middle of 326 (the material titled
*Indefinite Integrals: Formulas and Properties*) - Study Examples 2, 3
- Solve Matched Problems 2,3
- Solve Suggested Exercises 5.1 # 43, 45, 47, 49, 51, 53

Quiz 23 will be two problems involving indefinite integrals requiring the *Substitution Method*, based on Section 5.2 Suggested Exercises 5.2 # 11, 15, 17, 19, 23, 27, 29, 31, 33, 41

To prepare for Quiz 23

- The textbook’s presentation of the
*Substitution Method*in Section 5.2 is kind of a mess. Three different approaches are presented (in the subsections titled*Reversing the Chain Rule*and*Integration by Substition*and*Additional Substitution Techniques*) for different kinds of problems. This is silly. There only needs to be one approach for most problems. I think you would be better off NOT trying to read Section 5.2 of the textbook. - Read Class Notes from Friday, November 6 for a presentation of a straightforward approach to The
*Substitution Method*, an approach that works in all the problems that we will study in this course. The approach is outlined in Reference 8, found on page 7 of the Course Packet. - Study Class Drill 25 that was done in class on Friday, November 6.
- Study Examples 3, 4, 5 in the book. Try to do those examples with the method that I presented in class on Friday, November 6. Compare your solutions to the book’s solutions.
- Solve Matched Problems 3, 4, 5
- Solve Suggested Exercises 5.2 # 11, 15, 17, 19, 23, 27, 29, 31, 33, 41

Quiz 24 will be one ABCDE problem about the *Definite Integral* and *Riemann Sums*

To prepare for Quiz 24

- Read Class Notes from Tuesday, November 10 for an introduction to the definition of the
*Definite Integral*. - Study Class Drills 26 and 27, done in class on Tuesday, November 10.
- Read the textbook Section 5.4 pages 353 – 359.
- Study Example 3
- Solve Matched Problem 3
- Solve Suggested Exercises 5.4 # 15, 17, 19, 33, 41, 45, 49, 51, 53

Quiz 25 will be one ABCD problem about using the *Fundamental Theorem of Calculus* to evaluate *Definite Integrals*, based on Suggested Exercises 5.5 # 19, 21, 23, 25, 35, 36

*after* the quiz. This quiz problem is meant to test whether you have studied the book material that we are going to cover in class that day.

To prepare for Quiz 25

- Read the textbook Section 5.5 pages 363 – 365.
- Study Examples 1 and 2 in the book.
- Solve Matched Problems 1 and 2
- Solve Suggested Exercises 5.5 # 19, 21, 23, 25, 35, 36

Quiz 26 will be one question about the *Area Between Curves*. It will be based on Section 6.1 Examples 1, 3 and Suggested Exercises # 17, 55

This is material that we will start discussing in class *after* the quiz. This quiz is meant to test whether you have studied the book material that we are going to cover in class that day.

To prepare for Quiz 26

- Read the textbook Section 6.1 pages 382 - 384.
- Study Examples 1, 3
- Solve Matched Problems 1, 3
- Solve Suggested Exercises 6.1 # 17, 55

Quiz 27 will be based on Section 6.1 Examples # 4, 5 and Matched Problems # 4, 5, and Suggested Exercises 6.1 # 55, 67. The problem will be about the area of a region formed by two curves that intersect. In particular, the problem will involve determining the points of intersection.

To prepare for Quiz 27

- Read the textbook Section 6.1 pages 384 - 385.
- Study Examples 4, 5.
- Solve Matched Problems 4, 5
- Solve Suggested Exercises 6.1 # 55, 67

Notice that in the examples, the matched problems, and the two suggested exercises, you have to figure out where the graphs intersect and which graph is on top. Then you have to figure out how to set up the integrals.

Quiz 28 will be based on Section 6.2 Example # 4, Matched Problem # 4 and Suggested Exercises 6.2 # 55, 57, about Consumers’ Surplus.

This is material that we will start discussing in class *after* the quiz. This quiz is meant to test whether you have studied the book material that we are going to cover in class that day.

To prepare for Quiz 28

- Read Section 6.2 pages 397 – middle of 398. (In the subsection titled
*Consumers’ and Producers’ Surplus*, this is the material dealing with*Consumers’ Surplus*.) - Study Example 4.
- Solve Matched Problem 4
- Solve Suggested Exercises 6.2 # 55, 57

(page maintained by Mark Barsamian, last updated Aug 6, 2015