For this problem, consider the function 1 x-4 (a) Compute some derivatives at x = 5 and come up with a formula for the nth derivative f(n) (5). f(x) = (b) Write out the full Taylor series for f(x) centered at x = 5 in sigma notation. (c) Write out P3(2), the third-degree Taylor polynomial for f(x) centered at x = 5.
For this problem, consider the function 1 x-4 (a) Compute some derivatives at x = 5 and come up with a formula for the nth derivative f(n) (5). f(x) = (b) Write out the full Taylor series for f(x) centered at x = 5 in sigma notation. (c) Write out P3(2), the third-degree Taylor polynomial for f(x) centered at x = 5.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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Transcribed Image Text:For this problem, consider the function
1
x-4
(a) Compute some derivatives at x = 5 and come up with a formula for the nth derivative f(n) (5).
f(x) =
(b) Write out the full Taylor series for f(x) centered at x = 5 in sigma notation.
(c) Write out P3(2), the third-degree Taylor polynomial for f(x) centered at x = 5.
(d) Use Taylor's Remainder Theorem to estimate how close P3 (5.1) is to f(5.1).
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