![]() ![]() This means that you know how to interpret Lagrange and alternating series error bounds as the maximum error of an infinite series given a partial series.ģ) Identify a re-expression of mathematical information presented in a given representation. This means that you should know how to calculate the error bounds to analyze series, with the alternating error bound for alternating series and the Lagrange Error Bound for power series.Ģ) Explain how an approximated value relates to the actual value. Mathematical Practicesįour of the College Board's mathematical practices for AP Calculus are used in this unit, which are outlined below.ġ) Apply appropriate mathematical rules or procedures, with and without technology. The concepts in this unit may seem difficult at first, but with a little practice, you will be able to understand them. You will also need to understand the two types of error bounds you will encounter in this unit. It is important that you know the conditions for all the tests and what they tell you. You will learn 6 tests for different types of series to glean information about them. If you haven’t ever heard of analysis in a mathematical sense before, this is just the study of functions and how they behave over time. This unit emphasizes the study of series analysis. This unit builds from past knowledge of limits, differentiation, and integration, but applies this to a new concept - series. ![]() Well, after going through countless limits, derivatives, and integrals, you’ve made it here! Welcome to Unit 10, the last unit of AP Calculus BC! Before we move on, give yourself a pat on the back for all your hard work! □ Study AP Calculus, Unit 10.14: Finding Taylor or Maclaurin Series for a Functionġ2.Always one FRQ on this unit (usually FRQ 6) 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. □ Study AP Calculus, Unit 10.9: Determining Absolute or Conditional Convergenceġ1. 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. After doing this take the limit of the function as it goes to infinity. 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. This will then converge by the limit comparison test. 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. 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. ⛔ 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. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |