ao= a₁ = a2= a3 = 9. 9- a4 = (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)), y have found an estimate for the value of 7 in terms of an infinite series. Approximate the value of n 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.)
ao= a₁ = a2= a3 = 9. 9- a4 = (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)), y have found an estimate for the value of 7 in terms of an infinite series. Approximate the value of n 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
Related questions
Question
100%
s12
![(a) Evaluate the integral
48
S²
Your answer should be in the form kл, where k is an integer. What is the value of k?
darctan(z)
(Hint:
da
2²+1)
k =
ao
x² + 4
(b) Now, lets evaluate the same integral using power series. First, find the power series for the function f(x) = 84. Then, integrate it from 0 to 2, and call it S.
S should be an infinite series Σæ o an.
+4*
-0
What are the first few terms of S?
-dx.
a1 =
a₂ =
a3
a4 =
(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 7 in terms of an infinite series. Approximate the value of 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.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77f25919-c9cc-41ec-b3bf-4e76a5fe8c8e%2F46dc8ac6-6460-4e18-a24c-d0392e290b9a%2Fvmzu6w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Evaluate the integral
48
S²
Your answer should be in the form kл, where k is an integer. What is the value of k?
darctan(z)
(Hint:
da
2²+1)
k =
ao
x² + 4
(b) Now, lets evaluate the same integral using power series. First, find the power series for the function f(x) = 84. Then, integrate it from 0 to 2, and call it S.
S should be an infinite series Σæ o an.
+4*
-0
What are the first few terms of S?
-dx.
a1 =
a₂ =
a3
a4 =
(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 7 in terms of an infinite series. Approximate the value of 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.)
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