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In Example 6.22 part b, if you use the first 5 terms of the Maclaurin series (instead of the first 4 terms as in the example), what would the sum be? Answer with 4 decimal places. Note: All 4 decimal places might not be a correct approximation of the integral. Answer with 4 decimal places anyway.

In Example 6.22 part b, if you use the first 5 terms of the Maclaurin series (instead of the first 4 terms as in the example), what would the sum be? Answer with 4 decimal places. Note: All 4 decimal places might not be a correct approximation of the integral. Answer with 4 decimal places anyway.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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a. Express dx as an infinite series. b. Evaluate dx to within an error of 0.01. [Show/Hide Solution] Solution a. The Maclaurin series for e is given by (-a²)" 00 n! n=0 = 1- 22 - +.. +(-1)" + - 00 n! n=0 Therefore, 24 dx ... 2! 3! n! = C +x -+ +(-1)"- (2n+1)n! 3 5-2! 7-3! b. Using the result from part a. we have 1 1 e-" dx = 1 - + 3 10 1 1 42 216 The sum of the first four terms is approximately 0.74. By the alternating series test, this estimat is accurate to within an error of less than i6 0.0046296 < 0.01.
Transcribed Image Text:a. Express dx as an infinite series. b. Evaluate dx to within an error of 0.01. [Show/Hide Solution] Solution a. The Maclaurin series for e is given by (-a²)" 00 n! n=0 = 1- 22 - +.. +(-1)" + - 00 n! n=0 Therefore, 24 dx ... 2! 3! n! = C +x -+ +(-1)"- (2n+1)n! 3 5-2! 7-3! b. Using the result from part a. we have 1 1 e-" dx = 1 - + 3 10 1 1 42 216 The sum of the first four terms is approximately 0.74. By the alternating series test, this estimat is accurate to within an error of less than i6 0.0046296 < 0.01.
Read Example 6.22 in the textbook 2. In Example 6.22 part b, if you use the first 5 terms of the Maclaurin series (instead of the first 4 terms as in the example), what would the sum be? Answer with 4 decimal places. Note: All 4 decimal places might not be a correct approximation of the integral. Answer with 4 decimal places anyway.
Transcribed Image Text:Read Example 6.22 in the textbook 2. In Example 6.22 part b, if you use the first 5 terms of the Maclaurin series (instead of the first 4 terms as in the example), what would the sum be? Answer with 4 decimal places. Note: All 4 decimal places might not be a correct approximation of the integral. Answer with 4 decimal places anyway.
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