(a) Evaluate the integral 40 -dr. x2 + 4 Your answer should be in the form ka, where k is an integer. What is the value of k? d arctan(z) dz (Hint: %3D 12+1 k = (b) Now, lets evaluate the same integral using power series. First, find the power series for the function f(x) = 40. Then, integrate it from 0 to 2, and call it S. S should be an infinite series n-0 an· What are the first few terms of S? an = aj = az = az = as = (c) The answer in part (a) equals the sum of the infinite series in part (b) (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 7 by the first 5 terms. (d) What is an upper bound for your error of your estimate if you use the first 8 terms? (Use the alternating series estimation.)
(a) Evaluate the integral 40 -dr. x2 + 4 Your answer should be in the form ka, where k is an integer. What is the value of k? d arctan(z) dz (Hint: %3D 12+1 k = (b) Now, lets evaluate the same integral using power series. First, find the power series for the function f(x) = 40. Then, integrate it from 0 to 2, and call it S. S should be an infinite series n-0 an· What are the first few terms of S? an = aj = az = az = as = (c) The answer in part (a) equals the sum of the infinite series in part (b) (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 7 by the first 5 terms. (d) What is an upper bound for your error of your estimate if you use the first 8 terms? (Use the alternating series estimation.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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