Theorem 3.1. Let ƒ € C¹[a, b] and 0 < y < x be two real numbers. We have Σ f(n) = = 1₁² f* y
Theorem 3.1. Let ƒ € C¹[a, b] and 0 < y < x be two real numbers. We have Σ f(n) = = 1₁² f* y
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
Related questions
Question
![Theorem 3.1. Let ƒ € C¹[a, b] and 0 < y < x be two real numbers. We have
=
= [² [² (1
f(t)dt +
Y
Σ f(n)
y<n<x
S (t - [t]) f'(t)dt
− (x − [x])ƒ(x) + (y − [y])ƒ (y).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd57723e-bba5-4519-91be-cdc194b36b4f%2Fddc77830-0e18-4a23-97a7-65db3d4f5c43%2Flq6r09y_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Theorem 3.1. Let ƒ € C¹[a, b] and 0 < y < x be two real numbers. We have
=
= [² [² (1
f(t)dt +
Y
Σ f(n)
y<n<x
S (t - [t]) f'(t)dt
− (x − [x])ƒ(x) + (y − [y])ƒ (y).
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
![Elements Of Modern Algebra](https://www.bartleby.com/isbn_cover_images/9781285463230/9781285463230_smallCoverImage.gif)
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
![Elements Of Modern Algebra](https://www.bartleby.com/isbn_cover_images/9781285463230/9781285463230_smallCoverImage.gif)
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781938168383/9781938168383_smallCoverImage.gif)
![Trigonometry (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337278461/9781337278461_smallCoverImage.gif)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning