2. Taylor Series (a) Given the function ƒ : R \ {4} → R with f(x) = 4²x Determine a formula for the n-th derivative, show that this is valid for all nЄ N, and provide the Taylor series T[ƒ,0](x). Tip: First determine a few of the initial derivatives until you get a feel for the n-th derivative. (b) Given the function f : RR with f(x) = xex Determine a formula for the n-th derivative, show that this is valid for all nЄ N, and provide the Taylor series T[f, 0] (x). Simplify the series terms as much as possible.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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2. Taylor Series
(a) Given the function ƒ : R \ {4} → R with
f(x) = 4²x
Determine a formula for the n-th derivative, show that this is valid for all nЄ N, and provide the
Taylor series T[ƒ,0](x).
Tip: First determine a few of the initial derivatives until you get a feel for the n-th derivative.
(b) Given the function f : RR with
f(x) = xex
Determine a formula for the n-th derivative, show that this is valid for all nЄ N, and provide the
Taylor series T[f, 0] (x). Simplify the series terms as much as possible.
Transcribed Image Text:2. Taylor Series (a) Given the function ƒ : R \ {4} → R with f(x) = 4²x Determine a formula for the n-th derivative, show that this is valid for all nЄ N, and provide the Taylor series T[ƒ,0](x). Tip: First determine a few of the initial derivatives until you get a feel for the n-th derivative. (b) Given the function f : RR with f(x) = xex Determine a formula for the n-th derivative, show that this is valid for all nЄ N, and provide the Taylor series T[f, 0] (x). Simplify the series terms as much as possible.
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