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# ∙1.) (Cauchy form f defined f(n) exists (i) For each (ii) for of some. on and Taylor Thm) (a, b) Continuous on > ce (a, b). (a, b). x = (a, b), Rn (x) = Hint Induction and I. B. P. c = x < (a, b), Rn (x) = (x-c)⋅ (x-y)n-1 (n-1)! between y = √x (x-t√n-² JC (n-1)! f(n) (t) dt C, X f(n) (y)

# ∙1.) (Cauchy form f defined f(n) exists (i) For each (ii) for of some. on and Taylor Thm) (a, b) Continuous on > ce (a, b). (a, b). x = (a, b), Rn (x) = Hint Induction and I. B. P. c = x < (a, b), Rn (x) = (x-c)⋅ (x-y)n-1 (n-1)! between y = √x (x-t√n-² JC (n-1)! f(n) (t) dt C, X f(n) (y)

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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#1.) (Cauchy form f defined f(n) exists (i) For each (ii) of on and Hint: Induction c = x = (a, b) for some y Taylor Thm) (a, b) continuous on x = (a, b), Rn (x) = (x (x-t)^²+ с (n-1)! C € (a, b). (a, b). } and I. B. P. Rn (x) = (x-c)⋅ (x-y)n-² (n-1)! between f(n) (t) dt C, X f(n) (y)
Transcribed Image Text:#1.) (Cauchy form f defined f(n) exists (i) For each (ii) of on and Hint: Induction c = x = (a, b) for some y Taylor Thm) (a, b) continuous on x = (a, b), Rn (x) = (x (x-t)^²+ с (n-1)! C € (a, b). (a, b). } and I. B. P. Rn (x) = (x-c)⋅ (x-y)n-² (n-1)! between f(n) (t) dt C, X f(n) (y)
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