[4] [Computational cost as a function of error tolerance] Recall from Lecture 19 that the error in the Composite Trapezoidal Rule (CTR) using n subintervals of width h is given by -12²2 (6- 12 -(b − a) ƒ" (µ) (1) for some μ € (a, b). (a) Determine the values of n and h that are sufficient to approximate 2 S² x ln(x) dx (2) to within an error tolerance of T = 10-5; that is, determine n and h so that the absolute error when applying the CTR to (2) is smaller that 7. (Hint: take the absolute value of (1) and then say that the result is less than or equal to (1) when f"(µ) is replaced with the maximum value of |ƒ"(x)| on [1,2]. Then, determine n and h that make the resulting quantity less than 7). (b) Repeat part (a) for the case of Composite Simpson's Rule. For this integral, which method is superior?
[4] [Computational cost as a function of error tolerance] Recall from Lecture 19 that the error in the Composite Trapezoidal Rule (CTR) using n subintervals of width h is given by -12²2 (6- 12 -(b − a) ƒ" (µ) (1) for some μ € (a, b). (a) Determine the values of n and h that are sufficient to approximate 2 S² x ln(x) dx (2) to within an error tolerance of T = 10-5; that is, determine n and h so that the absolute error when applying the CTR to (2) is smaller that 7. (Hint: take the absolute value of (1) and then say that the result is less than or equal to (1) when f"(µ) is replaced with the maximum value of |ƒ"(x)| on [1,2]. Then, determine n and h that make the resulting quantity less than 7). (b) Repeat part (a) for the case of Composite Simpson's Rule. For this integral, which method is superior?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
Related questions
Question
Composite trapezoidal rule
![[4] [Computational cost as a function of error tolerance]
Recall from Lecture 19 that the error in the Composite Trapezoidal Rule
(CTR) using n subintervals of width h is given by
-h²
12
(b − a) ƒ" (µ)
for some μ € (a, b).
(a) Determine the values of n and h that are sufficient to approximate
2
[²₂
(1)
x ln(x) dx
(2)
to within an error tolerance of T = 10-5; that is, determine n and h so that
the absolute error when applying the CTR to (2) is smaller that 7.
(Hint: take the absolute value of (1) and then say that the result is less
than or equal to (1) when f"(µ) is replaced with the maximum value of
|ƒ"(x)| on [1,2]. Then, determine n and h that make the resulting quantity
less than 7).
(b) Repeat part (a) for the case of Composite Simpson's Rule. For this
integral, which method is superior?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fd47556-f3ce-4f39-818d-be563d9523c8%2F2f268b73-e390-4850-aef1-9631e70a938b%2Fbvblqla_processed.png&w=3840&q=75)
Transcribed Image Text:[4] [Computational cost as a function of error tolerance]
Recall from Lecture 19 that the error in the Composite Trapezoidal Rule
(CTR) using n subintervals of width h is given by
-h²
12
(b − a) ƒ" (µ)
for some μ € (a, b).
(a) Determine the values of n and h that are sufficient to approximate
2
[²₂
(1)
x ln(x) dx
(2)
to within an error tolerance of T = 10-5; that is, determine n and h so that
the absolute error when applying the CTR to (2) is smaller that 7.
(Hint: take the absolute value of (1) and then say that the result is less
than or equal to (1) when f"(µ) is replaced with the maximum value of
|ƒ"(x)| on [1,2]. Then, determine n and h that make the resulting quantity
less than 7).
(b) Repeat part (a) for the case of Composite Simpson's Rule. For this
integral, which method is superior?
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