(a) Give the second-order Taylor polynomial T₂ (2) for the function f (x) = x¹/2, about a = 9. (b) Use Taylor's Theorem to give the Error Term E₂ (x) = f (x) - T₂ (x), as a function of x and some z between 9 and x. (Note that here we are using z instead of which is used in the notes). (c) Give an upper bound for the error |E2 (12)|.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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(a) Give the second-order Taylor polynomial T₂ (x) for the function ƒ (x) = x¹/2, about a = 9.
(b) Use Taylor's Theorem to give the Error Term E₂ (x) = f (x) – T₂ (x), as a function of a and some z between 9 and x. (Note that here we are using z
instead of which is used in the notes).
(c) Give an upper bound for the error |E2 (12)|.
Transcribed Image Text:(a) Give the second-order Taylor polynomial T₂ (x) for the function ƒ (x) = x¹/2, about a = 9. (b) Use Taylor's Theorem to give the Error Term E₂ (x) = f (x) – T₂ (x), as a function of a and some z between 9 and x. (Note that here we are using z instead of which is used in the notes). (c) Give an upper bound for the error |E2 (12)|.
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