Calculus for Business, Economics, and the Social and Life Sciences, Brief Version, Media Update (2022)

Calculus for Business, Economics, and the Social and Life Sciences, Brief Version, Media Update (1)

11th Edition

By Laurence Hoffmann and Gerald Bradley and David Sobecki and Michael Price
ISBN10: 007353238X
ISBN13: 9780073532387
Copyright: 2013

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The estimated amount of time this product will be on the market is based on a number of factors, including faculty input to instructional design and the prior revision cycle and updates to academic research-which typically results in a revision cycle ranging from every two to four years for this product. Pricing subject to change at any time.

  • TABLE OF CONTENTS
  • AUTHOR BIOS

Chapter 1: Functions, Graphs, and Limits

1.1Functions

1.2The Graph of a Function

1.3Lines and Linear Functions

1.4Functional Models

1.5Limits

1.6One-Sided Limits and Continuity

Chapter 2: Differentiation: Basic Concepts

2.1The Derivative

2.2Techniques of Differentiation

2.3Product and Quotient Rules; Higher-Order Derivatives

2.4The Chain Rule

2.5Marginal Analysis and Approximations Using Increments

2.6Implicit Differentiation and Related Rates

Chapter 3: Additional Applications of the Derivative

3.1 Increasing and Decreasing Functions; Relative Extrema

3.2 Concavity and Points of Inflection

3.3 Curve Sketching

3.4 Optimization; Elasticity of Demand

3.5 Additional Applied Optimization

Chapter 4: Exponential and Logarithmic Functions

4.1 Exponential Functions; Continuous Compounding

4.2 Logarithmic Functions

4.3 Differentiation of Exponential and Logarithmic Functions

4.4 Additional Applications; Exponential Models

Chapter 5: Integration

5.1 Indefinite Integration and Differential Equations

5.2 Integration by Substitution

5.3 The Definite Integral and the Fundamental Theorem of Calculus

5.4 Applying Definite Integration: Distribution of Wealth and Average Value

5.5 Additional Applications to Business and Economics

5.6 Additional Applications to the Life and Social Sciences

Chapter 6: Additional Topics in Integration

6.1 Integration by Parts; Integral Tables

6.2 Numerical Integration

6.3 Improper Integrals

6.4 Introduction to Continuous Probability

Chapter 7: Calculus of Several Variables

7.1 Functions of Several Variables

7.2 Partial Derivatives

7.3 Optimizing Functions of Two Variables

7.4 The Method of Least-Squares

7.5 Constrained Optimization: The Method of Lagrange Multipliers

7.6 Double Integrals

Appendix A: Algebra Review

A.1 A Brief Review of Algebra

A.2 Factoring Polynomials and Solving Systems of Equations

A.3 Evaluating Limits with L’Hopital’s Rule

A.4 The Summation Notation

About the Author

Laurence Hoffmann

Laurence D. HoffmannNovember 2011I consider myself to be a writer and expositor as well as a mathematician, and these traits led to the original version of this text published in 1975. Before assuming my current position as a Senior Investment Management Consultant with Morgan Stanley Smith Barney, I was a tenured professor of mathematics at Claremont McKenna College, where, on three occasions, I was honored to be the recipient of the Huntoon Award for Excellence in Teaching, a “best-teacher” award determined by a vote of the students.In addition to my current profession and my ongoing involvement with this text, I serve on the Strategic Planning committee of the Claremont Community foundation and on the Investment Committee of the Rancho Santa Ana Botanic Gardens in Claremont.My wife, Janice, and I love to travel, enjoy music and the arts, have two grown sons, three grandchildren and two Maltese dogs. I am an avid (but average) tennis player, am addicted to the Sunday Puzzle on NPR, and have been trying for several years to become fluent in Italian.Long ago, I received by BA in mathematics from Brown University and my Ph.D. in mathematics from the University of Wisconsin.

Gerald Bradley

After receiving my undergraduate degree at Harvey Mudd College and my PhD from Caltech, I joined the Mathematics Department at Claremont McKenna College, where I have continued to teach, specializing in calculus, linear algebra, and differential equations. I love to write, and in addition to this text have written published texts on engineering calculus and linear algebra.My wife, Jaqui, and I are active supporters of recording textbooks for the blind and dyslexic. We also travel whenever we get a chance and especially enjoy cruising. Our favorite destinations have been Crete, Barcelona, and Singapore. I’m a lifelong Boston Red Sox, Los Angeles Lakers, and USC Trojan football fan, and write science fiction novels in my spare time. We have two sons, a newborn grandson, and seven cats, although it’s not clear whether we have the cats or they have us. We also raise foster kittens for a local shelter until they are ready to be adopted, and yes, three of our cats are fosters that we could not resist adopting ourselves.

David Sobecki

I was born and raised in Cleveland, and started college at Bowling Green State University in 1984 majoring in creative writing. Eleven years later, I walked across the graduation stage to receive a PhD in math, a strange journey indeed. After two years at Franklin and Marshall College in Pennsylvania, I came home to Ohio, accepting a tenure-track job at the Hamilton campus of Miami University. I’ve won a number of teaching awards in my career, and while maintaining an active teaching schedule, I now spend an inordinate amount of time writing textbooks and course materials. I’ve written or co-authored either seven or twelve textbooks, depending on how you count them, as well as several solutions manuals and interactive CD-ROMS.After many years as developmental math coordinator at Miami Hamilton, I share the frustration that goes along with low pass rates in the developmental math curriculum. Far too many students end up on the classic Jetson’s-style treadmill, with the abstract nature of the traditional algebra curriculum keeping them from reaching their goals. Like so many instructors across the country, I believe the time is right to move beyond the one-size-fits-all curriculum that treats students the same whether they hope to be an engineer or a pastry chef. “Because we’ve always done it that way” is NOT a good reason to maintain the status quo in our curriculum. Let’s work together to devise alternate pathways that help students to learn more and learn better while hastening their trip into credit-bearing math courses. Since my book (Math in Our World) is written for the Liberal Arts Math and Quantitative Literacy market, I think I’m in the right place at the right time to make a difference in the new and exciting pathways course.I’m in a very happy place right now: my love of teaching meshes perfectly with my childhood dream of writing. (Don’t tell my publisher this – they think I spend 20 hours a day working on textbooks – but I’m working on my first novel in the limited spare time that I have.) I’m also a former coordinator of Ohio Project NExT, as I believe very strongly in helping young college instructors focus on high-quality teaching as a primary career goal. I live in Fairfield, Ohio with my lovely wife Cat and fuzzy dogs Macleod and Tessa. When not teaching or writing, my passions include Ohio State football, Cleveland Indians baseball, heavy metal music, travel, golf, and home improvement.

Michael Price

Michael Price is a senior instructor and assistant department head of mathematics at the University of Oregon in Eugene, Oregon. Both his undergraduate and graduate degrees are from the University of Oregon, where has worked as a graduate student and instructor for the last 9 years. Michael has taught courses in introductory and intermediate algebra, up through precalculus, statistics, and three variations of calculus aimed at, respectively, biology/human physiology, business/economics, and mathematics/physical science students. As a coordinator for the precalculus sequence at the U of O and periodically other sequences required for non-math majors, Michael spends a substantial portion of his time developing and reinforcing responsible course material for mathematics service courses. In addition to this textbook, he has also contributed to supplemental materials and reviews of undergraduate texts in mathematics.

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TABLE OF CONTENTS

Chapter 1: Functions, Graphs, and Limits

1.1Functions

1.2The Graph of a Function

1.3Lines and Linear Functions

1.4Functional Models

1.5Limits

1.6One-Sided Limits and Continuity

Chapter 2: Differentiation: Basic Concepts

2.1The Derivative

2.2Techniques of Differentiation

2.3Product and Quotient Rules; Higher-Order Derivatives

2.4The Chain Rule

2.5Marginal Analysis and Approximations Using Increments

2.6Implicit Differentiation and Related Rates

Chapter 3: Additional Applications of the Derivative

3.1 Increasing and Decreasing Functions; Relative Extrema

3.2 Concavity and Points of Inflection

3.3 Curve Sketching

3.4 Optimization; Elasticity of Demand

3.5 Additional Applied Optimization

Chapter 4: Exponential and Logarithmic Functions

4.1 Exponential Functions; Continuous Compounding

4.2 Logarithmic Functions

4.3 Differentiation of Exponential and Logarithmic Functions

4.4 Additional Applications; Exponential Models

Chapter 5: Integration

5.1 Indefinite Integration and Differential Equations

5.2 Integration by Substitution

5.3 The Definite Integral and the Fundamental Theorem of Calculus

5.4 Applying Definite Integration: Distribution of Wealth and Average Value

5.5 Additional Applications to Business and Economics

5.6 Additional Applications to the Life and Social Sciences

Chapter 6: Additional Topics in Integration

6.1 Integration by Parts; Integral Tables

6.2 Numerical Integration

6.3 Improper Integrals

6.4 Introduction to Continuous Probability

Chapter 7: Calculus of Several Variables

7.1 Functions of Several Variables

7.2 Partial Derivatives

7.3 Optimizing Functions of Two Variables

7.4 The Method of Least-Squares

7.5 Constrained Optimization: The Method of Lagrange Multipliers

7.6 Double Integrals

Appendix A: Algebra Review

A.1 A Brief Review of Algebra

A.2 Factoring Polynomials and Solving Systems of Equations

A.3 Evaluating Limits with L’Hopital’s Rule

A.4 The Summation Notation

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AUTHOR BIOS

About the Author

Laurence Hoffmann

Laurence D. HoffmannNovember 2011I consider myself to be a writer and expositor as well as a mathematician, and these traits led to the original version of this text published in 1975. Before assuming my current position as a Senior Investment Management Consultant with Morgan Stanley Smith Barney, I was a tenured professor of mathematics at Claremont McKenna College, where, on three occasions, I was honored to be the recipient of the Huntoon Award for Excellence in Teaching, a “best-teacher” award determined by a vote of the students.In addition to my current profession and my ongoing involvement with this text, I serve on the Strategic Planning committee of the Claremont Community foundation and on the Investment Committee of the Rancho Santa Ana Botanic Gardens in Claremont.My wife, Janice, and I love to travel, enjoy music and the arts, have two grown sons, three grandchildren and two Maltese dogs. I am an avid (but average) tennis player, am addicted to the Sunday Puzzle on NPR, and have been trying for several years to become fluent in Italian.Long ago, I received by BA in mathematics from Brown University and my Ph.D. in mathematics from the University of Wisconsin.

Gerald Bradley

After receiving my undergraduate degree at Harvey Mudd College and my PhD from Caltech, I joined the Mathematics Department at Claremont McKenna College, where I have continued to teach, specializing in calculus, linear algebra, and differential equations. I love to write, and in addition to this text have written published texts on engineering calculus and linear algebra.My wife, Jaqui, and I are active supporters of recording textbooks for the blind and dyslexic. We also travel whenever we get a chance and especially enjoy cruising. Our favorite destinations have been Crete, Barcelona, and Singapore. I’m a lifelong Boston Red Sox, Los Angeles Lakers, and USC Trojan football fan, and write science fiction novels in my spare time. We have two sons, a newborn grandson, and seven cats, although it’s not clear whether we have the cats or they have us. We also raise foster kittens for a local shelter until they are ready to be adopted, and yes, three of our cats are fosters that we could not resist adopting ourselves.

David Sobecki

I was born and raised in Cleveland, and started college at Bowling Green State University in 1984 majoring in creative writing. Eleven years later, I walked across the graduation stage to receive a PhD in math, a strange journey indeed. After two years at Franklin and Marshall College in Pennsylvania, I came home to Ohio, accepting a tenure-track job at the Hamilton campus of Miami University. I’ve won a number of teaching awards in my career, and while maintaining an active teaching schedule, I now spend an inordinate amount of time writing textbooks and course materials. I’ve written or co-authored either seven or twelve textbooks, depending on how you count them, as well as several solutions manuals and interactive CD-ROMS.After many years as developmental math coordinator at Miami Hamilton, I share the frustration that goes along with low pass rates in the developmental math curriculum. Far too many students end up on the classic Jetson’s-style treadmill, with the abstract nature of the traditional algebra curriculum keeping them from reaching their goals. Like so many instructors across the country, I believe the time is right to move beyond the one-size-fits-all curriculum that treats students the same whether they hope to be an engineer or a pastry chef. “Because we’ve always done it that way” is NOT a good reason to maintain the status quo in our curriculum. Let’s work together to devise alternate pathways that help students to learn more and learn better while hastening their trip into credit-bearing math courses. Since my book (Math in Our World) is written for the Liberal Arts Math and Quantitative Literacy market, I think I’m in the right place at the right time to make a difference in the new and exciting pathways course.I’m in a very happy place right now: my love of teaching meshes perfectly with my childhood dream of writing. (Don’t tell my publisher this – they think I spend 20 hours a day working on textbooks – but I’m working on my first novel in the limited spare time that I have.) I’m also a former coordinator of Ohio Project NExT, as I believe very strongly in helping young college instructors focus on high-quality teaching as a primary career goal. I live in Fairfield, Ohio with my lovely wife Cat and fuzzy dogs Macleod and Tessa. When not teaching or writing, my passions include Ohio State football, Cleveland Indians baseball, heavy metal music, travel, golf, and home improvement.

Michael Price

Michael Price is a senior instructor and assistant department head of mathematics at the University of Oregon in Eugene, Oregon. Both his undergraduate and graduate degrees are from the University of Oregon, where has worked as a graduate student and instructor for the last 9 years. Michael has taught courses in introductory and intermediate algebra, up through precalculus, statistics, and three variations of calculus aimed at, respectively, biology/human physiology, business/economics, and mathematics/physical science students. As a coordinator for the precalculus sequence at the U of O and periodically other sequences required for non-math majors, Michael spends a substantial portion of his time developing and reinforcing responsible course material for mathematics service courses. In addition to this textbook, he has also contributed to supplemental materials and reviews of undergraduate texts in mathematics.

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FAQs

Is calculus for business easier than calculus? ›

Nobody would call any kind of calculus course easy. But, most students would tell you that business calculus is a bit easier than calculus since there is less of a focus on theory and there are less rules to learn for derivatives and integrals.

Is business economics a lot of math? ›

There are many diagrams in economics, but there is not a large amount of math. A proviso: The amount of math in the economics curriculum varies across colleges and universities. Some economics departments do not require their students to learn much math or statistics, but others do.

What is calculus for business and social science? ›

It is intended primarily for students in the fields of business and social science. The emphasis is on skill-building and on applications of calculus to the areas of business, economics, and social science. The types of functions studied include polynomials, rational, exponential, and logarithmic.

Do you need calculus 3 for economics? ›

The minimal math background for any prospective graduate student in economics is Calculus I-III, Linear Algebra, a probability course (3000 level or higher) and a statistics course (3000 level or higher).

How do you pass business calculus? ›

How to Pass Calculus
  1. Get Ready to Study. Effectively studying calculus can take a lot of time. ...
  2. Work with Other Students. You should try to make use of study groups if you can. ...
  3. Give Yourself Time. Make sure you give yourself enough time to study for your exams. ...
  4. Complete Practice Problems. ...
  5. Use Online Resources.

Do I need pre calc for business calculus? ›

Business calculus isn't as difficult as the regular calculus that most applied science majors need to know, but you would still need a foundation in pre-calc to understand it, and taking precalc in college would probably be harder than taking it in high school.

Is economics harder than math? ›

Economics is not harder than Maths. In fact, maths is one of the hardest and most challenging majors. Most students struggle with maths because it is a highly abstract subject and has many tough concepts and ideas. Economics is a hard subject but not quite as difficult as maths.

Do I need to be good at math to study economics? ›

Graduate courses generally require a very strong math background—at least through multivariable calculus and in some cases real analysis—and a lot more work than a 3000-level or 4000-level Economics course. Please note that Independent Study courses (ECON 4999) can never be counted toward the Economics major.

Can I study economics without maths? ›

Dear Aspirant yes you can do Ba economics without mathematics as compulsory subject in class 12. for any further query feel free to ask! hope it helps!

Is calculus in economics hard? ›

Economics involves a lot of fairly easy calculus rather than a little very hard calculus. Primarily, this means calculation of simple derivatives and the occasional bit of integration. Doing economics is a great way to become good at calculus! You will get lots of exposure to simple calculus problems.

Is college calculus hard? ›

Calculus is expected to be difficult; it should not be impossible. But, too often, this course becomes a gatekeeper that pushes students out of careers in science, technology, engineering and math — or STEM — fields, especially women and marginalized students.

Do I need calculus to get into college? ›

Calculus isn't actually required to get into most colleges. Fewer than 5 percent of respondents to a survey—all at private institutions—said calculus was a blanket requirement for all or most majors.

What topics are covered in business calculus? ›

  • 4 Credits.
  • Functions. – Inequalities and lines. – Exponents. ...
  • Derivatives. – Limits. – ...
  • Application of the Derivative. – Graphing using: – ...
  • Exponential and Logarithmic Functions. – Algebraic properties review. – ...
  • Integration. – Antiderivatives and Indefinite integrals. – ...
  • Multivariable calculus. – Functions of several variables. –

What do you learn in calculus for business? ›

Course Description:

This course is the basic study of limits and continuity, differentiation, optimization and graphing, and integration of elementary functions, with emphasis on applications in business, economics, and social sciences.

What class is math 1332? ›

This course includes an introduction to treatments of sets, logic, number systems, number theory, relations, functions, probability, and statistics. Appropriate applications are included.

What percentage of people fail calculus? ›

Calculus Is the Gateway Course for STEM Majors

For the 66 percent of students who pass calculus, they can go on to take more advanced coursework in their field. On the other hand, the 34 percent who fail calculus may retake the class until they pass or change their major to one that doesn't require calculus.

How do I study for a calculus exam in one day? ›

These six steps will help you study for an exam in 24 hours or less.
  1. Make a list of important terms, concepts, and ideas.
  2. Look for summaries in the textbook.
  3. Make more notes as you go.
  4. Make use of mind maps, charts, and graphs.
  5. Teach a friend.
  6. Review your important terms lists.
  7. Study out of order.
  8. Take practice tests.
13 Jun 2022

Why is calculus so hard? ›

Most of the reasons students have difficulty learning calculus is because they don't study daily after lessons, can't focus in class, have gaps in their math knowledge, and think learning calculus is a waste of time. Here are the steps you can take to make calculus a breeze: Stay curious. Ask questions.

Should I skip precalculus? ›

you can def skip trig/precalc and go straight to calc. as long as you can use a unit circle, you should be fine with the trig. precalc spends weeks on the first thing you learn in calc1, so it's pretty much a big waste of time.

How fast can you learn calculus? ›

How Long Will It Take? Depending on your reason for learning calculus, the length in which you achieve your goal will vary. But if you want to gain a foundational understanding of the subject so that you can move on to more challenging courses, then give yourself at least four to six months.

How do I get good at calculus? ›

How to improve grades in calculus – 13 Tips
  1. Establish a solid foundation. ...
  2. Do insightful studying. ...
  3. Understand the concept of limits. ...
  4. Grasp the fundamental theorems of calculus. ...
  5. List things to memorize. ...
  6. Understand the problem-solving approach during class. ...
  7. Solve a load of new problems. ...
  8. Analyze and understand every mistake.
12 Apr 2022

Why is economics hard to study? ›

A college-level economics class can be challenging because you need to grasp new concepts like supply and demand, scarcity, diminishing returns, and opportunity costs. It requires you learn new vocabulary and to use critical thinking skills. But those theories, concepts, and terms build upon one another.

Which is harder economics or physics? ›

Theoretical economics goes into number theory, topology, and game theory, but it's less about the math and more about mathematically describing a (usually) relatively simple idea. Overall, I would say physics is "mathier."

Can I self learn economics? ›

There are basically two major ways by which one can self learn economics. The first and the most efficient way is to enroll in a Massive Open Online Course (MOOC). They are a fun and usually free source of knowledge. Alternatively, you could also read some books on economics.

What type of math is used in economics? ›

Although economics graduate programs have varying admissions requirements, graduate training in economics is highly mathematical. Most economics Ph. D. programs expect applicants to have had advanced calculus, differential equations, linear algebra, and basic probability theory.

Do you have to be good at math to major in business? ›

There are many applications for strong math skills in the business world. Business majors who wish to focus on finance careers will need a strong calculus background. Knowledge of statistics and probability are also vital for finance careers, and figure prominently in the marketing field too.

Is finance a lot of math? ›

Some of the main math-related skills that the financial industry requires are: mental arithmetic (“fast math”), algebra, trigonometry, and statistics and probability. A basic understanding of these skills should be good enough and can qualify you for most finance jobs.

What careers dont need maths? ›

Here is a list of distance learning courses you can study without maths:
  • Bookkeeping and Accounting Studies.
  • Forensics and Investigations.
  • Policing, Forensics and Investigation Studies.
  • Office Administration and Secretarial Studies.
  • Business Management Studies.
  • Beauty Therapy Studies.
  • Occupational Health and Safety Studies.
6 Sept 2022

Which courses can I do without maths? ›

Courses After 12th Commerce Without Maths
  • B.Com (Bachelor of Commerce) ...
  • B.Com (H) (Bachelor of Commerce Honors) ...
  • BBA (Bachelor of Business Administration) ...
  • LLB (Bachelor in Law / Legum Baccalaureus) ...
  • CA (Chartered Accountancy) ...
  • CMA (Certified Management Accountancy) ...
  • CS (Company Secretary)
4 Oct 2022

What courses dont require math? ›

Online Degrees That Don't Require Math
  • Anthropology.
  • Communications.
  • Criminal Justice.
  • Culinary Arts.
  • Education.
  • English.
  • Foreign Language.
  • Graphic Design.
25 May 2022

What kind of math is business calculus? ›

Business Calculus I covers one-variable calculus and some multivariable calculus. The course stresses applications in business and economics, and is intended to give business students the appropriate conceptual and computational mathematical background for future study in business.

What is taught in business calculus? ›

Topics include relations and functions, limits, continuity, derivatives, techniques of differentiation, chain rule, applications of differentiation, antiderivatives, the definite integral, the fundamental theorem of calculus, and applications of integration.

What is the point of business calculus? ›

Business calculus is necessary when calculating optimum production quantities which will result in the greatest profit. It is also used to calculate the profit on additional items made (marginal profit). Another use is in determining ideal packaging and shipment sizes. There are many other uses.

What topics are covered in business calculus? ›

  • 4 Credits.
  • Functions. – Inequalities and lines. – Exponents. ...
  • Derivatives. – Limits. – ...
  • Application of the Derivative. – Graphing using: – ...
  • Exponential and Logarithmic Functions. – Algebraic properties review. – ...
  • Integration. – Antiderivatives and Indefinite integrals. – ...
  • Multivariable calculus. – Functions of several variables. –

How difficult is calculus? ›

For most students, calculus is an extremely hard and challenging course of study. For math majors, it is the introduction to higher-level mathematics. If you are planning to pursue a math degree then calculus will be one of the easier courses that you take during your freshman and sophomore years.

Do you need to be good at math for business? ›

There are many applications for strong math skills in the business world. Business majors who wish to focus on finance careers will need a strong calculus background. Knowledge of statistics and probability are also vital for finance careers, and figure prominently in the marketing field too.

Is statistics more difficult than calculus? ›

Statistics does tend to be harder than calculus, especially at the advanced levels. If you take a beginning statistics course, there will be very simple concepts that are rather easy to work out and solve.

Is business statistics hard in college? ›

Business statistics is not necessarily hard, but it can be complex. Business statistics begins with very fundamental statistical techniques, such as regression and calculations of covariance. These skills are needed in many fields, including all forms of scientific research.

What's the difference between analysis and calculus? ›

Analysis is the branch of mathematics that underpins the theory behind the calculus, placing it on a firm logical foundation through the introduction of the notion of a limit. This module introduces differentiation and integration from this rigourous point of view.

Is college algebra hard to learn? ›

College Algebra is not difficult if you've taken Pre-Algebra and Algebra in the past and done well. However, if you haven't done well, or it's a been a while since you've taken Pre-Algebra and Algebra, College Algebra will be difficult.

How is calculus used in business and economics? ›

Calculus, by determining marginal revenues and costs, can help business managers maximize their profits and measure the rate of increase in profit that results from each increase in production. As long as marginal revenue exceeds marginal cost, the firm increases its profits.

Is applied calculus the same as calculus 1? ›

Applied Calculus does not lead to the higher Calculus sequence, and is not equivalent to the higher Calculus I course. Applied Calculus is usually the last math course a student takes as an undergraduate. Applied Calculus does not include nor require Trigonometry.

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