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✪ Re-read Example 2 carefully. Then repeat these two calculations using [x³dx instead of Show your work on the back of this sheet. -dx.

✪ Re-read Example 2 carefully. Then repeat these two calculations using [x³dx instead of Show your work on the back of this sheet. -dx.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
Example 2 How large should we taken in order to guarantee that the Trapezoidal and Midpoint Rule approximations for rf(1/2) de are accurate to within 0.0001? Solution We saw in the preceding calculation that|f" (z)| < 2 for 1 < x < 2, so we can take K = 2, a = 1, and b = 2 in (3), Accuracy to within 0.0001 means that the size of the error should be less than 0.0001. Therefore we choose n so that Solving the inequality for n, we get or Thus n = 41 will ensure the desired accuracy. 2(1)³ 12m² 11² which gives <0.0001 2 12(0.0001) 1 ✓0.0006 Note It's quite possible that a lower value for n would suffice, but 41 is the smallest value for which the error bound formula can guarantee us accuracy to within 0.0001. For the same accuracy with the Midpoint Rule we choose n so that 2(1)³ 24m² 40.8 <0.0001 1 ✓0.0012 29
Transcribed Image Text:Example 2 How large should we taken in order to guarantee that the Trapezoidal and Midpoint Rule approximations for rf(1/2) de are accurate to within 0.0001? Solution We saw in the preceding calculation that|f" (z)| < 2 for 1 < x < 2, so we can take K = 2, a = 1, and b = 2 in (3), Accuracy to within 0.0001 means that the size of the error should be less than 0.0001. Therefore we choose n so that Solving the inequality for n, we get or Thus n = 41 will ensure the desired accuracy. 2(1)³ 12m² 11² which gives <0.0001 2 12(0.0001) 1 ✓0.0006 Note It's quite possible that a lower value for n would suffice, but 41 is the smallest value for which the error bound formula can guarantee us accuracy to within 0.0001. For the same accuracy with the Midpoint Rule we choose n so that 2(1)³ 24m² 40.8 <0.0001 1 ✓0.0012 29
Ⓒ Re-read Example 2 carefully. Then repeat these two calculations using [x³dx instead of Show your work on the back of this sheet. dx.
Transcribed Image Text:Ⓒ Re-read Example 2 carefully. Then repeat these two calculations using [x³dx instead of Show your work on the back of this sheet. dx.
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