Part Bof the attach question 216(a) Evaluate the integral:dax² + 4Your answer should be in the form ka, where k is an integer. What is the value of k?d1-arctan(x)dxHint:x² + 1k =(b) Now, let's evaluate the same integral using a power series. First, find the power series for the16function f(x) =. Then, integrate it from 0 to 2, and call the result S. S should be an infinite2² + 4'series.What are the first few terms of S?= Opaj =a2 =az =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 r by the first 5 terms.(d) What is the upper bound for your error of your estimate if you use the first 7 terms? (Use thealternating series estimation.)

Given, fx=16x2+4 Now we shall express the given integrand as the sum of power series. 16x2+4=1641+x2416x2+4=41+x2416x2+4=4∑n=0n=∞-x24n16x2+4=41-x24+x442-x6x3+x8x4 . . . Now we shall integrate it from 0 to 2, ∫0216x2+4dx=4∫021-x24+x442-x6x3+x8x4 . . . dxS=4x-x33+x554-x7742. . . . 02S=8-83+3220-128112+512576 . . . . Hence we get, a0=8a1=-83a2=3220a3=-128112a4=512576

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(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 2² + 4' series. What are the first few terms of S? = Op = lp az = a4 =

(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 2² + 4' series. What are the first few terms of S? = Op = lp az = a4 =

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question 21 V939.64 O True False
14: Answer c questions
For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C. View the rubric linked above for help if needed. For Part A, Part B, and Part C, use the scenario below. Show all work. Cards are drawn from a standard 52-card deck without replacement. Part A: Two cards are drawn. What is the probability that the first card is a five and the second card is a six? Part B: Two cards are drawn. What is the probability that both cards are fives? Is the probability that both cards are fives greater or less than the probability that a five and six are drawn? Explain. Part C: Three cards are drawn. What is the probability that exactly two cards are fives?