A Evaluate The Integral K Your Answer Should Be In The Form Km Where K Is An Integer What Is The Value Of K D 1 1 (48.81 KiB) Viewed 12 times
A Evaluate The Integral K Your Answer Should Be In The Form Km Where K Is An Integer What Is The Value Of K D 1 2 (45.26 KiB) Viewed 12 times
(a) Evaluate the integral: k= = Your answer should be in the form km, where k is an integer. What is the value of k? d 1 Hint: arctan(2) da x² + 1 a1 = a2 = (b) Now, let's evaluate the same integral using a power series. First, find the power series for the funct Then, integrate it from 0 to 2, and call the result S. S should be an infinite series. 48 f(x) = a3 = 2 · 1² x² + 4 04 == = . What are the first few terms of S? ao= 48 x² + 4 da (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 π in terms of an infinite series. Approximate the value of π by the first 5 terms. (d) What is the upper bound for your error of your estimate if you use the first 10 terms? (Use the alternating series estimation.)
a1 = a2 = a3 = 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 10 terms? (Use the alternating series estimation.) Question Help: Video Submit Question 1,728 JUL LO 5 tv (a 2 A A @
Join a community of subject matter experts. Register for FREE to view solutions, replies, and use search function. Request answer by replying!