(a) Evaluate the integral: SHint: -arctan(r)Your answer should be in the form kπ, where k is an integer. What is the value of k?d1dxx² +1k(b) Now, let's evaluate the same integral using a power series. First, find the power series for the functionThen, integrate it from 0 to 2, and call the result S. S should be an infinite series.16f(x) =x² + 4What are the first few terms of S?aoa1a2a3a4||||16x² + 4||||dr||(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 7 in terms of an infinite series.Approximate the value of by the first 5 terms.(d) What is the upper bound for your error of your estimate if you use the first 11 terms? (Use thealternating series estimation.)

Answered: Image /qna-images/answer/cc090c5e-dbba-4316-a30f-e4ec80e82870.jpg

(a) Evaluate the integral: S Hint: Your answer should be in the form ki, where k is an integer. What is the value of k? d 1 -arctan(r) dx ²+1 k (b) Now, let's evaluate the same integral using a power series. First, find the power series for the function Then, integrate it from 0 to 2, and call the result S. S should be an infinite series. 16 f(x)= x²+4 What are the first few terms of S? ao a1 a2 a3 || || 16 x² + 4 || || dr 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 in terms of an infinite series. Approximate the value of by the first 5 terms. (d) What is the upper bound for your error of your estimate if you use the first 11 terms? (Use the alternating series estimation.)

(a) Evaluate the integral: S Hint: Your answer should be in the form ki, where k is an integer. What is the value of k? d 1 -arctan(r) dx ²+1 k (b) Now, let's evaluate the same integral using a power series. First, find the power series for the function Then, integrate it from 0 to 2, and call the result S. S should be an infinite series. 16 f(x)= x²+4 What are the first few terms of S? ao a1 a2 a3 || || 16 x² + 4 || || dr 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 in terms of an infinite series. Approximate the value of by the first 5 terms. (d) What is the upper bound for your error of your estimate if you use the first 11 terms? (Use the alternating series estimation.)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.1: Infinite Sequences And Summation Notation

Problem 73E

See similar textbooks