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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) +

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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)
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)
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