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(1 point) Use Maclaurin series to calculate the given limit. Tables of series have been provided...
Use the given Maclaurin series to evaluate the limit. x - ln (1 + x) lim x-0 ex - 1 - x
Previous Problem Problem List Next Problem 4n + (1 point) Use the limit comparison test to determine whether Ž. - converges 1412 p. converge or diverges. (a) Choose a series br with terms of the form bn = and apply the limit comparison test. Write your answer as a fully reduced fraction. For n > 14, lim = lim 1+00 1 00 (b) Evaluate the limit in the previous part. Enter op as infinity and -o as-infinity. If the limit...
(1 point) The series is an alternating series but we can apply the ratio test to to test for absolute convergence. Applying the ratio test for absolute convergence you would compute lim (k+1 = li k00 ak k- 00 Hence the series converges Note that you will have to simplify your answer for the limit or you will get an error message.
(1 point) The three series ^A,, ^ Bn, and > Cn have terms 1 An n 1 В, %3 1 С, —- = Use the Limit Comparison Test to compare the following series to any of the above series. For each of the series below, you must enter two letters. The first is the letter (A,B, or C) of the series above that it can be legally compared to with the Limit Comparison Test. The second is C if the...
( 7n3 +1 (1 point) Consider the series > 1. Evaluate the the following limit. If it is infinite, = ( 2n3 + 3) type "infinity" or "inf". If it does not exist, type "DNE". lim vanl = 1 n-> Answer: L = What can you say about the series using the Root Test? Answer "Convergent", "Divergent", or "Inconclusive". Answer: choose one Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Answer "Absolutely Convergent", "Conditionally Convergent", or "Divergent"....
Please answer all parts. (1 point) Series: A Series (Or Infinite Series) is obtained from a sequence by adding the terms of the sequence. Another sequence associated with the series is the sequence of partial sums. A series converges if its sequence of partial sums converges. The sum of the series is the limit of the sequence of partial sums For example, consider the geometric series defined by the sequence Then the n-th partial sum Sn is given by tl...
(1 point) The three series [ An, Bn, and Cn have terms 1 1 An = Bn = 1 n4' Cn n6' n Use the Limit Comparison Test to compare the following series to any of the above series. For each of the series below, you must enter two letters. The first is the letter (A, B, or C) of the series above that it can be legally compared to with the Limit Comparison Test. The second is C if...
Write VBA functions to calculate sin (x) using the Maclaurin arcsine series, and compare the values for sin-1(x) from your program to those given by the Excel spreadsheet function ASIN(x). The Maclaurin arcsine expansion is given by x 3x 6 40 (2n)! sin1(x)-2((2n+1) Note: This function by definition is only defined for-1 SxS1. When you write the code for calculating it, you will need to include code that assigns a value to it that reflects it is undefined for values...
(1 point) Test each of the following series for convergence by either the Comparison Test or the Limit Comparison Test. If at least one test can be applied to the series, enter CONV if it converges or DIV if it diverges. If neither test can be applied to the series, enter NA. (Note: this means that even if you know a given series converges by some other test, but the comparison tests cannot be applied to it, then you must...
At least one of the answers above is NOT correct (1 point) Test each of the following series for convergence by either the Comparison Test or the Limit Comparison Test. If at least one test can be applied to the series, enter CONV if it converges or DIV if it diverges. If neither test can be applied to the series, enter NA. (Note this mearns that even if you know a given series converges by some other test, but the...