Q.10. Q.10./ Let [a, b] be an interval of R. Let f[a,b] R be a function such that f is M-times differentiable in [a, b] and (m + 1) times differen- tiable in (a, b), then prove that: \m f(b)= f(a)+(b − a)Dƒ (a) +...+(b − a)" where (b-a)(m+1) (m+1) ce(a,b). -Dm f(c) ·Dm f(a) +
Q.10. Q.10./ Let [a, b] be an interval of R. Let f[a,b] R be a function such that f is M-times differentiable in [a, b] and (m + 1) times differen- tiable in (a, b), then prove that: \m f(b)= f(a)+(b − a)Dƒ (a) +...+(b − a)" where (b-a)(m+1) (m+1) ce(a,b). -Dm f(c) ·Dm f(a) +
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.4: Definition Of Function
Problem 54E
Related questions
Question
Urgent help
![Q.1
Q.10./ Let [a, b] be an interval of R. Let
f[a,b]R be a function such that f is M-times
auc
differentiable in [a, b] and (m + 1) times differen-
tiable in (a, b), then prove that:
f(b)=f(a)+(b-a) Df (a)+...+(b-a) Dm f(a)+
(b-a)(m+1)
(m+1)
where ce(a,b).
m
-Dm f(c)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf2e1c02-7674-4b64-9596-6a5b4e135f3a%2F37edd2d2-caa3-4b70-9ee2-6f818fe6d3bd%2Fgk6v42i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q.1
Q.10./ Let [a, b] be an interval of R. Let
f[a,b]R be a function such that f is M-times
auc
differentiable in [a, b] and (m + 1) times differen-
tiable in (a, b), then prove that:
f(b)=f(a)+(b-a) Df (a)+...+(b-a) Dm f(a)+
(b-a)(m+1)
(m+1)
where ce(a,b).
m
-Dm f(c)
Expert Solution
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
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage