0 X MC Home - montgomerycollege.edu x VA Section 5.9 Exercises" Fall 2021 - X Course Hero X G Use the Trapezoidal Rule, the Mic X + C webassign.net/web/Student/Assignment-Responses/last?dep=27869826 Z . .. Apps MC MyMC Login (80) YouTube History t Evaluate the defini... M Gmail YouTube Translate Cengage Single Sig.. C Home - Credo Refe.. Health Coverage Af.. Google Docs Reading list ULTAILS UCALCUL4 J..AL.VZ. IVIT NOTES Video Example '() EXAMPLE 2 How large should we take n in order to guarantee that the Trapezoidal and Midpoint Rule approximations for the integral below are accurate to within 0.00003? SOLUTION If f(x) = 1/x, then f '(x) = , and f " (x) = Since 1 S x S 2, we have /x 1, so If " ( x ) 1 = 1 We take K = 2, a = 1, and b = 2. Accuracy to within 0.00003 means that the size of the error should be less than 0.00003. Therefore we chose n so that 12(0.00003) or n > 74.54 V0.00018 Thus n = will ensure the desired accuracy. For the same accuracy with the Midpoint Rule we choose n so that V12 . 0.00003 Need Help? Read It0 X MC Home - montgomerycollege.edu x VA Section 5.9 Exercises" Fall 2021 - X *Course Hero X G Use the Trapezoidal Rule, the Mic X + F C webassign.net/web/Student/Assignment-Responses/last?dep=27869826 Z Apps MC MyMC Login (80) YouTube History t Evaluate the defini... M Gmail YouTube Translate Cengage Single Sig.. |Home - Credo Refe.. Health Coverage Af.. Google Docs > Reading list 2. [-/1 Points] DETAILS SCALCCC4 5.9.AE.03. MY NOTES EXAMPLE 3 (a) Use the Midpoint Rule with n = 10 to approximate the integral. y = ex2 (b) Give an upper bound for the error involved in this approximation. SOLUTION (a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives = Ax[ f(0.05 ) + F( ) + ...+ f( ) + f(0.95)] = 0.1[@0.0025 + el 1+ 0.0625 + el + 0.2025 + 20.3025+ el + 20.5625 + el + 20.9025] Video Example () The figure illustrates this approximation. (b) Since O(x) = e", we have O'(x) = and "(x) = Also, since 0 S x S 1 we have x s and so osf" ( x ) = S be Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your answer to five decimal places.) 6e . 1 (10)2 Need Help? Read It