Chapter 2: Limits and Continuity



Dear Parents of 2013-2014 Advanced Placement Calculus AB students,I would like to take the opportunity to welcome you and your son/daughter to the Advanced Placement Calculus AB class at Oxford High School. This is my 4th year to teach AB Calculus and my 6th year to teach BC Calculus, and I am looking forward to a successful but hard-working year. I have high expectations for my students both in class and on the AP exam that is administered in May. I will also prepare your student for his/her college course of study and urge your child to keep all of his/her high school Calculus work for a reference in college. By attending the College Board training institute, our class includes extensive real-world problems such as population growth, drug absorption rates, stress of construction materials, etc., that reflect the spirit of the reform in the calculus curriculum. Calculus has stood the test of time and continues to be the foundation of modern mathematics as well as engineering, biological, and social sciences. By allowing students the use of a graphing calculator, the College Board has been able to add approximately one-third new material to the Advanced Placement Calculus exams and make the test more relevant to today’s world by drawing attention more to ideas than techniques. It is no longer a question of “whether or not technology,” but rather a question of how will we use it. In my calculus class, I will be using the TI-84 graphing calculator to enhance our graphical and numerical understanding of each concept. For the AP exam, students are required to bring two graphing calculators. Although I am not familiar enough with using the TI-89 or the TI-Inspire calculator to teach using it in class, it does give a student a distinct advantage over the student using the TI-83 or TI-84. Therefore, I have plenty of materials that will help your son/daughter if he/she chooses to use the TI-89 or the TI-Inspire. However, a TI-83 or TI-84 is appropriate for the graphing calculator on the exam. Again, it is my responsibility to provide students with the information, concepts, and skills to perform at a high level in this class as well as on the AP exam. However, it is his/her responsibility to maintain the discipline and accountability for themselves to reach the goals we have in this class. I look forward to a wonderful year, and hopefully, above all else, we will all become better people for our community.Sincerely,Chris BaughmanAP CALCULUS AB CLASS PROCEDURES & EXPECTATIONSTEXTBOOK:? Calculus: Graphical, Numerical, Algebraic. Finney, Demana, Waits, Kennedy. Reading, Mass.: Addison-Wesley, 2007.DOWNLOADABLE TEXTBOOK/RESOURCES: Website: HYPERLINK "" Code: azk-1003PRIMARY REVIEW BOOK ($16 due by Feb.): AP Test Prep Series: AP Calculus for Calculus: Graphical, Numerical, Algebraic. Barton, Brunsting, Diehl, Hill, Tyler, Wilson. Boston, Mass.: Addison-Wesley, 2007. HOMEWORK WEBSITE: EQUIPMENT NEEDED: Students will be expected to bring their textbook, graphing calculator (TI-84, TI-84 Plus, or TI-89), notebook/binder, and pencil every day. GRADING POLICIES:?The grading scale I use throughout the school year is similar to the system used to grade the AP exam. The grading system is as follows: All decimal answers must be correct to three decimal places with appropriate units labeled (when applicable) to receive full credit. Each multiple-choice question will be worth 2 points.? Each free response problem consisting of one single part will be worth 5 points.? Each free response problem with multiple parts will be worth 9 points.?The same grading system will be used on all assignments (tests, quizzes, and labs) except for homework.?? HOMEWORK:? Homework is an integral part of learning mathematics. Practice problems will be given daily and should take approximately 60 – 75 minutes to complete. I encourage students to attempt every problem assigned.? It is permissible to discuss problems with other students, relatives, or tutors.? It is not permissible to copy another student's work.? Each student should do his or her best to think through the problems and develop an understanding of the concepts. If you should need help on any particular problem outside of class, I can work through problems and make those available on my Haiku web page as well as Show Me (see “Other Useful Sites/Apps”).??? Suggested homework problems that will help with online homework problems will be discussed daily.? Students need to always be sure to correct homework problems, as it will help comprehension of the material.? Required homework problems given from Web Assign must be completed by the due date and will be graded for correctness.?? Homework will be posted on the board as well as on my Haiku web page.AP PROBLEM OF THE WEEK: On chosen weeks, students will be given an “AP Problem of the Week.” Each problem will be a question used on previous AP Calculus exams. The students will be given the problem on Monday or Tuesday of each week. Friday, the students will be given the first part of class to work the problem taken for a grade. This gives each student the opportunity to discuss the problem with peers and research the solution during the week. The more experience students can receive working practice AP exam problems, the better prepared they will be for the exam in the spring. Although the concepts involved in the problems will remain the same, the “Friday version” of the problem may have some numerical alterations. AP problems of the week will be posted on my Haiku web page.GROUP WORK:? Several times each nine weeks, students will work in collaborative groups. All group members are expected to participate to complete the assigned activity.? The assignment may consist of past AP exam problems, calculator/computer labs, or projects.?Sometimes, one paper (agreed upon by all group members) will be collected and graded as a representation of the entire group.? If a group cannot come to a consensus, then each member may turn in his/her own solution.? TESTS/QUIZZES:? Test will be given at the end of each chapter and may also be administered in the middle of a chapter.? Each test will consist of both multiple choice questions and free response items (consistent with the AP exam). A nine weeks' test may be given at the end of the first and third nine weeks.? A student may replace his/her lowest test grade with the nine weeks' test grade.? Quizzes will be given often. If the teacher feels an ample number of quizzes were given in a nine weeks, he may drop a student’s lowest quiz grade.NINE WEEKS' GRADES:? Grades will be calculated on a total point basis.? Each activity will be assigned a certain number of points.? At the end of the nine weeks, the final nine weeks’ average will be calculated according to the following grading scale: tests and projects will be counted four times in Power School, quizzes will be counted three times, labs will be counted twice, and homework and AP Problems of the Week will be counted once.MAKE -UP WORK:? If a student is absent he/she must make up the work within 3 days. It is the student's responsibility to see me about make-up work when he/she returns from an absence.? If arrangements have not been made within three days, zeros will be recorded for all work missed.? Make-up tests will be given before school whenever possible to avoid having to miss another class discussion.? Good attendance is of utmost importance in this class.? I realize that sometimes absences are necessary, but I encourage you to keep them at a minimum.? If at any point a student needs extra help from me, I am available Monday mornings from 6:30 until 7:15 (duty) and any other mornings from 6:30 until 7:40. EXTRA CREDIT:? Extra credit may be offered each grading period at the teacher’s discretion.? AP EXAM ?DATE:? Wednesday, May 7, 2013 at 8:00 am (You will be allowed to take two calculators into the exam room.)?TEST FORMAT:28 Multiple Choice questions without calculator (55 minutes) 17 Multiple Choice questions with graphing calculator (50 minutes) 2 Free Response questions with graphing calculator (30 minutes) 4 Free Response questions without calculator (60 minutes) HAIKU: To access my Haiku teacher web page:1.) Go to .) Type in the following code to enroll: 5YP2V3.) Click on Student4.) Click on Register and enter your information5.) Read terms of service and mark the box saying you have done so.6.) Click Create Account7.) Once an account has been created, to sign back into the website, go to and click on Sign In at the top.OTHER USEFUL SITES/APPS FOR CLASS: (search for Chris Baughman)You Tube (Khan Academy videos)Remind101Send a text message to (610) 365-1777 with the message @abcal4?YOU MUST BE ABLE TO DO THE FOLLOWING WITH YOUR CALCULATOR: ? 1.? Produce a graph of a function. ? 2.? Find the solution of an equation. ? 3.? Find the derivative of a function at a particular point. ? 4.? Find the definite integral of a function. ??????? (Memories will not be erased.) ?ALLOWABLE CALCULATORS: ?CASIO???????????????????????????? HP???? RADIO SHACK?????????????? SHARP?????? TI ?FX 6000???? FX7500????? HP 28?????? EC 4033??????????????????????? EL 5200?????????? TI 80 ?FX 6200???? FX7700????? HP 48?????? EC 4034??????????????????????? EL 9200?????????? TI 81 ?FX 6300???? FX8000????? HP 38G??? EC4037???????????????????????? EL 9300?????????? TI 82 ?FX 6500???? FX8500???????????????????????????????????????????????????????????????????????????????? ???? TI 83 ?FX 7000???? FX8700???????????????????????????????????????????????????????????????????????????????????? TI 85 ?FX8800????? FX9700???????????????????????????????????????????????????????????????????????????????????? TI 86 ?CFX-9800 CFX9850?????????????????????????????????????????????????????????????????????????????????? TI 89????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? TI 83 Plus?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ??? TI 84TUTORING/EXTRA ASSISTANCE: Students are expected to collaborate with each other within and outside of the classroom. I am available most mornings for extra assistance beginning at 6:30 AM. However, Monday mornings I have duty in the gymnasium, and once or twice a month I will have administrative meetings. Other opportunities to receive tutoring also exist through Ole Miss or other former educators as well as through my BC students and former students. TEACHER CONTACT INFORMATION:Chris Baughmancbaughman@ ORcgbaughm@ School Phone: 234–1562Cell Phone: 801–8782AB CALCULUS CURRICULUM PLANChapter 1: Prerequisites for Calculus The students will:Represent functions numerically, graphically, algebraically, and verbally.Classify and graph the elementary functions: power, root, polynomial, rational, algebraic, and transcendental (exponential, logarithmic, trigonometric, and inverse trigonometric).Transform functions by shifting, stretching, and reflecting.Analyze the differences in graphs of f(x), f(x), and f(x) .Define inverse functions and form function compositions.Analyze and graph planar curves including those given in parametric form, polar form, and vector form.Chapter 2: Limits and Continuity The students will:Calculate limits using algebra.Estimate limits from graphs or tables of data.Determine asymptotic behavior graphically and by using infinite limits analysis.Determine the continuity of a function at a point.Apply graphical interpretations of continuity as in the Intermediate Value Theorem and the Extreme Value Theorem.Determine the tangent line to a given curve.Apply rate of change to find the slope of a curve at a point.Chapter 3: Derivatives The students will:Define the derivative as a limit of the difference quotient.Interpret the derivative as an instantaneous rate of change.Relate the concepts of differentiability and continuity.Find the slope of a curve at a point and use it to write an equation of a tangent line, if one exists.Use the tangent line as a linear approximation.Approximate rate of change from graphs and data.Use differentiation rules for sums, products, quotients, and compositions involving the elementary functions of single variable calculus.Use the Chain Rule to differentiate.Differentiate implicitly defined functions.Differentiate parametric, polar, and vector functions.Differentiate trigonometric, inverse trigonometric, exponential, and logarithmic functions.Chapter 4: Applications of Derivatives The students will:Use f’ and f” to analyze the graph of f, monotonicity, concavity, extrema, and points of inflection.Find corresponding characteristics between graphs of f, f’, and f”.Use the Mean Value Theorem and know its geometric consequences.Optimize, finding both absolute and relative extrema.Model rates of change, including related rates.Use the derivative in the study of motion: speed, velocity, and acceleration.Chapter 5: The Definite Integral The students will:Compute Riemann sums using left, right, and midpoint evaluation points.Recognize the definite integral as a limit of Riemann sums over equal subdivisions.Interpret the definite integral of the rate of change of a quantity over an interval as the change of the quantity over the interval.Use basic properties of definite integrals.Use the Fundamental Theorem of Calculus to evaluate definite integrals.Use the Fundamental Theorem to represent a particular antiderivative, and the analytical and graphical analysis of functions so defined.Find antiderivatives analytically including a substitution of variables technique.Use Riemann and trapezoidal sums to approximate definite integrals of functions represented algebraically, geometrically, and by tables and use error analysis to solidify approximationsAntidifferentiate using integration by parts and partial fractions techniques.Chapter 7: Applications of Definite Integrals The students will:Use integrals to model physical, social, or economic pute area of a pute volumes of solids of revolution and volumes of solids with known cross sections.Determine the average value of a function over an interval and understand the geometric interpretation of average value.Use the integral of a rate of change to give accumulated pute arc length (function or parametric).Compute polar area.Chapter 6: Differential Equations and Mathematical Modeling The students will:Write equations involving derivatives from verbal descriptions (and vice versa).Find specific antiderivatives using boundary conditions.Solve separable differential equations and use them in modeling.Interpret differential equations geometrically via slope fields.REVIEW FOR AP EXAM ................
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