![]() □ Study AP Calculus, Unit 10.14: Finding Taylor or Maclaurin Series for a Functionġ2. A Taylor series that is specifically centered at 0 is called a _ series.Īnswer: This series is called a Maclaurin series and is important to recognize since sometimes on the AP test they will tell you it is a Maclaurin series! You are expected to know it is centered at 0. ![]() Limits and Continuity About 47 of the questions on your exam will cover Limits and Continuity. □ Study AP Calculus, Unit 10.9: Determining Absolute or Conditional Convergenceġ1. Infinite Sequences and Series: 1718 of test questions This guide offers an overview of the main tested subjects, along with sample AP multiple-choice questions that look like the questions you’ll see on test day. On the contrary if the absolute value diverges and the series converges then the series conditionally converges. This is called _.Īnswer: If both converge this is called absolue convergence. If the absolute value of a series converges then the regular series must also converge. From this value take the absolue value and this should give you zero which means it converges since it is less than 1.ġ0. Does ) 1 1 + k ( k 2 k 1 have a sum How does the result of part a help to answer this question Determine whether each series converges or diverges. After doing this take the limit of the function as it goes to infinity. n Your calculator shows that 1 1 1 k ( k + 1 ) 2 2 ( n + 1 ). How do we know when the ratio test is inconclusive?Īnswer: Take out the n from both the numerator and denominator then take the square root of the whole function. □ Study AP Calculus, Unit 10.7: Alternating Series Test for ConvergenceĨ. The limit of the series to infinity is zero and the series is a decreasing sequence.Īnswer: Both of these must hold true for the series and it must have an alternator of some sort. The limit of the series to infinity is not zero and the series is an increasing sequence.ĭ. The limit of the series to infinity is zero and the series is an increasing sequence.Ĭ. The limit of the series to infinity is not equal to zero and the series is a decreasing sequence.ī. An alternating series converges if both of the conditions are satisfied. □ Study AP Calculus, Unit 10.6: Comparison Tests for Convergenceħ. of infinite sequences and infinite series to a well-defined limit. This will then converge by the limit comparison test. Calculus is the mathematical study of continuous change, in the same way that geometry is. How do we know when a series diverges by the nth term test?Īnswer: Compare this function to 1/n^2 which is a p series and converges. The nth term test only tests for divergence. □ Study AP Calculus, Unit 10.2: Working with Geometric SeriesĢ. If r is greater than 1 than it is an exponential growth function. AP Calculus BC AP Calculus BC Exam Questions AP Calculus BC Past Exam Questions Free-Response Questions Download free-response questions from past exams along with scoring guidelines, sample responses from exam takers, and scoring distributions. It is an exponential function so if the rate is less than one that is an exponential decay function. greater than one less than or equal to oneĪnswer: Think about how a geometric series would look. less than one greater than or equal to one.Ĭ. For the geometric series test, the series converges when the absolute value of r is _ and diverges when the absolute value of the rate is _.ī. *The following questions were not written by CollegeBoard and although they cover information outlined in the AP Calculus AB/BC Course and Exam Description, the formatting on the exam may be different.ġ. This means it should take you about 35 minutes to complete 15 questions. Click here for the practice questions: AP Calculus Unit 10 Multiple Choice Questions.įacts about the test: Both the AP Calculus AB and BC exams have 45 multiple-choice questions and you will be given 1 hour and 45 minutes to complete the section. ![]() III.⛔ STOP!⛔ Before you look at the answers make sure you gave this practice quiz a try so you can assess your understanding of the concepts covered in unit 10. ![]() Applications of Integration (Chapter 6). ![]() Separation of Variables and Logistic Equation.Differential Equations: Growth and Decay.Antiderivatives and Indefinite Integration.Applications of Differentiation (Chapter 3).Definition of Derivative and Rates of Change.Finding Limits Graphically and Numerically.Limits and Their Properties (Chapter 1).Then we will study the topics that are new to Calculus BC, Chapter 6-9 This information will be taken from Chapters 1-5 in the textbook. BC ONLY: LIM-8.D.1 A power series is a series of the form, where n is a non-negative integer, is a sequence of real numbers, and r is a real number. Note: We will begin by review what was taught in AP Calculus AB this will be called Calculus AB Review. 10.13 Radius and Interval of Convergence of a Power Series BC ONLY LEARNING OBJECTIVE LIM-8.D Determine the radius of convergence and interval of convergence for a power series. ![]()
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