40dx+ 4(a) Evaluate the integral:Your answer should be in the form ka, where k is an integer. What is the value of k?d1arctan(x)dxHint:x2 + 1k(b) Now, let's evaluate the same integral using a power series. First, find the power series for the function40f(x) =7. Then, integrate it from 0 to 2, and call the result S. S should be an infinite series.x2 + 4What are the first few terms of S?= Opai =азa4(c) The answers to part (a) and (b) are equal (why?). Hence, if you divide your infinite series from (b) byk (the answer to (a)), you have found an estimate for the value of T in terms of an infinite series.Approximate the value of T by the first 5 terms.(d) What is the upper bound for your error of your estimate if you use the first 9 terms? (Use thealternating series estimation.)

Hey, since there are multiple subparts posted, we will answer the first question. If you want any…

40 (a) Evaluate the integral: / da x2 + 4 Your answer should be in the form kT, where k is an integer. What is the value of k? d 1 -arctan(x): dx Hint: x2 + 1 k = 5 (b) Now, let's evaluate the same integral using a power series. First, find the power series for the function 40 f(x) = 7. Then, integrate it from 0 to 2, and call the result S. S should be an infinite series. x2 + 4 What are the first few terms of S? ao = a2 аз a4 = (c) The answers to part (a) and (b) are equal (why?). Hence, if you divide your infinite series from (b) by k (the answer to (a)), you have found an estimate for the value of T in terms of an infinite series. Approximate the value of T by the first 5 terms. ||

40 (a) Evaluate the integral: / da x2 + 4 Your answer should be in the form kT, where k is an integer. What is the value of k? d 1 -arctan(x): dx Hint: x2 + 1 k = 5 (b) Now, let's evaluate the same integral using a power series. First, find the power series for the function 40 f(x) = 7. Then, integrate it from 0 to 2, and call the result S. S should be an infinite series. x2 + 4 What are the first few terms of S? ao = a2 аз a4 = (c) The answers to part (a) and (b) are equal (why?). Hence, if you divide your infinite series from (b) by k (the answer to (a)), you have found an estimate for the value of T in terms of an infinite series. Approximate the value of T by the first 5 terms. ||

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.1: Equations

Problem 75E

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