Given a function ?=4cos(?)y=4cos⁡(x), where we are working in RADIANS, answer the following:For all numerical answers, answer to within 3 decimal places.Note that adatpive marking has been used to consider the method mark. c)Using the Maclaurin series up to, and including, the 3rd term, calculate theapproximate gradient of y at x = 0.2.d)Given the answer to the integrals from parts a) and b) are not the same, which of thefollowing are true?O Whilst there are errors in the approximated integral, the relative errors willgenerally decrease if the Maclaurin series included more than the three termsused here.O Reducing the upper limit of the integral will reduce the error.O The Maclaurin series is an approximation to y, hence the integrals of y and itsTaylor expansion will be different.O Approximating the integrals between the limits [T, 7] using the Maclaurinseries from part a) is appropriate.O Increasing the limits of the integral will have no effect on the accuracy of theintegral. Given a function y = 4 cos(x), where we are working in RADIANS, answer the following:For all numerical answers, answer to within 3 decimal places.Note that adatpive marking has been used to consider the method mark.a)Calculate the approximate integral of-0.3So" y(x)dxwhen y(x) is represented by its Maclaurin series up to, and including, the 3rd term.b)What is the absolute difference between your answer in a) and the exact integral of0.3Lo" y(x)dx ?

Answered: Image /qna-images/answer/ce87e1f6-0327-45dd-889f-f72ac10abcd6.jpg

Given a function y 4 cos(x), where we are working in RADIANS, answer the following: For all numerical answers, answer to within 3 decimal places. Note that adatpive marking has been used to consider the method mark. a) Calculate the approximate integral of •0.3 S y(x)dx when y(x) is represented by its Maclaurin series up to, and including, the 3rd term. b) What is the absolute difference between your answer in a) and the exact integral of 0.3 y(x)dx ?

Given a function y 4 cos(x), where we are working in RADIANS, answer the following: For all numerical answers, answer to within 3 decimal places. Note that adatpive marking has been used to consider the method mark. a) Calculate the approximate integral of •0.3 S y(x)dx when y(x) is represented by its Maclaurin series up to, and including, the 3rd term. b) What is the absolute difference between your answer in a) and the exact integral of 0.3 y(x)dx ?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.4: Total Differentials And Approximations

Problem 14E: Use the total differential to approximate each quantity. Then use a calculator to approximate the...

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