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16 (a) Evaluate the integral: dr 1² + 4 Your answer should be in the form ka, where k is an integer. What is the value of k? d -arctan(r) 1 Hint: dr 1² +1 k = 2 (b) Now, let's evaluate the same integral using a power series. First, find the power series for the 16 function f(x) = . Then, integrate it from 0 to 2, and call the result S. S should be an infinite 1² + 4 series. What are the first few terms of S? ao = | 8 32 a2 20 128 az = 12 512 576 a4 = of ||

16 (a) Evaluate the integral: dr 1² + 4 Your answer should be in the form ka, where k is an integer. What is the value of k? d -arctan(r) 1 Hint: dr 1² +1 k = 2 (b) Now, let's evaluate the same integral using a power series. First, find the power series for the 16 function f(x) = . Then, integrate it from 0 to 2, and call the result S. S should be an infinite 1² + 4 series. What are the first few terms of S? ao = | 8 32 a2 20 128 az = 12 512 576 a4 = of ||

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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16 (a) Evaluate the integral: dx x² + 4 Your answer should be in the form kn, where k is an integer. What is the value of k? d 1 -arctan(r) da Hint: x² + 1 k 2 (b) Now, let's evaluate the same integral using a power series. First, find the power series for the function f(x) = 16 Then, integrate it from 0 to 2, and call the result S. S should be an infinite x² + 4 series. What are the first few terms of S? ao = 8 a1 = 3 32 20 128 az = 12 512 576 a4 =
Transcribed Image Text:16 (a) Evaluate the integral: dx x² + 4 Your answer should be in the form kn, where k is an integer. What is the value of k? d 1 -arctan(r) da Hint: x² + 1 k 2 (b) Now, let's evaluate the same integral using a power series. First, find the power series for the function f(x) = 16 Then, integrate it from 0 to 2, and call the result S. S should be an infinite x² + 4 series. What are the first few terms of S? ao = 8 a1 = 3 32 20 128 az = 12 512 576 a4 =
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