Rolla Let X, Y be Banach spaces and U be an open subset of X. Letf: U→Ybe (n + 1)-times continuously differentiable mapping of U into Y. Then, if thesegment joining a and a + h is in U, we have11_f(a+h) = f(a) + f'(a)h + — ƒ" (a)h(²) + ... + ¹ f(n) (a) h(n)[2f"nHere h(n)= (h.h...h), n-times.+1·(1-t) f(n+¹)(a + th) h(n+1)ndt.

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Answered: Let X, Y be Banach spaces and U be an…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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Let X, Y be Banach spaces and U be an open subset of X. +1)-times continuously differentiable mapping of U into ent joining a and a + h is in U, we have 1 f(a+h) = f(a) + f'(a)h + ¹ ƒ" (a) h (²) + ... + ¹ f(n) (a)