![]() ![]() Let h be a function for which all derivatives exist at x = 1. The third-order Taylor polynomial P 3 ( x) for sin x about isĤ8. Determine the convergence or divergence of the sequence with the. If the sequence converges, find its limit. Determine the convergence or divergence of the sequence with the given nth term. (C) If the terms of an alternating series decrease, then the series converges.Ĥ7. converges both p-series and Integral Test d. (B) If a series is truncated after the nth term, then the error is less than the first term omitted. two sequences previously assigned to the basement ( Adie, 1964 ) are now. (A) If converges, then so does the series including in the Trinity Peninsula Series of the Antarctic Peninsula. Which of the following statements is true? Which of the following alternating series diverges?Ģ6. For which of the following series does the Ratio Test fail?Ģ5. Which of the following series diverges?Ģ4. Which of the following series converges?Ģ3. (E) Rearranging the terms of a positive convergent series will not affect its convergence or its sum.Ģ2. (D) If 1000 terms are added to a convergent series, the new series also converges. (C) If and converge, so does where c ≠ 0. Answers for integrals, derivatives, limits, sequences, sums, products, series expansions, vector analysis. Which of the following statements about series is false? Calculus and analysis calculators and examples. Directions: Some of the following questions require the use of a graphing calculator.Ģ1. Replace the first sentence in Question 19 by “Let f be the Taylor polynomial P 9 ( x) of order 9 for tan −1 x about x = 0.” Which choice given in Question 19 is now the correct one? Then it follows that, if −0.5 tan −1 x if x 0Ģ0. Let f be the Taylor polynomial P 7 ( x) of order 7 for tan −1 x about x = 0. ![]() If the series tan −1 is used to approximate with an error less than 0.001, then the smallest number of terms needed isġ9. If an appropriate series is used to evaluate then, correct to three decimal places, the definite integral equalsġ8. The coefficient of x 4 in the Maclaurin series for f ( x) = e − x /2 isġ7. arn1 converges when r < 1, otherwise diverges. Which of the following expansions is impossible?ġ6. A series is conditionally convergent when an is divergent but an is convergent. Which of the following series diverges?ġ3. Which of the following series diverges?ġ1. Which of the following statements about series is true?ġ0. is a series of constants for which Which of the following statements is always true?ĩ. Which of the following sequences diverges?ĥ. Review of sequences will enhance understanding of series.Ĥ. We have nevertheless chosen to include the topic in Questions 1–5 because a series and its convergence are defined in terms of sequences. Note: No questions on sequences will appear on the BC examination. Directions: Answer these questions without using your calculator. Need some help studying? Check out this sample of Kaplan’s Rapid Review Live.Calculus AB and Calculus BC CHAPTER 10 Sequences and Series If you have an idea about which colleges you want to go to, check out their websites or call the admissions office to find their particular rules regarding AP scores. Many colleges and universities will give you college credit for a score of 3 or higher, but some require a 4 or a 5. Your results will be placed into one of the following categories, reported on a five-point scale (relative to receiving college credit or advanced placement): We will also briefly discuss how to determine if an infinite series will converge or diverge (a more in depth discussion of this topic will occur in the next section). We will also give many of the basic facts, properties and ways we can use to manipulate a series. After a bit of a wait, your composite score will arrive. Series The Basics In this section we will formally define an infinite series. The multiple-choice part is handled by a machine, while qualified readers-current and former calculus teachers and professors-grade your responses to Section II. Unit 10 study guides written by former AP Calc students to review Infinite Sequences & Series (BC Only) with detailed explanations and practice questions. When your three-plus hours of testing are up, your exam is sent away for grading. You should not spend too much time on any one problem. Therefore, you should answer every question, even if you have to guess.įor the Free Response section, all problems are given equal weight, but the individual parts of a particular problem are not necessarily given equal weight. No points are awarded for unanswered questions. no points are deducted for wrong answers. If it produces a positive finite value, the original series acts the same as the reduced one. Then take the limit as x of the two series divided. Scores are based on the number of questions answered correctly. Simplify the series by only looking at the leading term in the numerator and denominator. ![]()
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