The Taylor polynomial of degree 100 for the function fabout x = 3 is given by P (x) = (x – 3)² – (2–3)4 (x–3)® (x–3)100 n+1 (x-3)²" +(-1)"+1 n! + %3| + +.... ... 2! 3! 50! What is the value of f(24) (3)? 1 24! 24! 12! 1 24! 24! 12! 1 12!

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 22RE
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The Taylor polynomial of degree 100 for the function fabout x = 3 is given by
(x–3)®
%3D
(x–3)4
(x–3)10
P (x) = (x – 3)² –
+...+ (–1)"+1 (x-3)²n
+ •
-
2!
3!
n!
50!
What is the value of f (24) (3)?
1
24!
24!
12!
1
24!
24!
12!
1
12!
Transcribed Image Text:The Taylor polynomial of degree 100 for the function fabout x = 3 is given by (x–3)® %3D (x–3)4 (x–3)10 P (x) = (x – 3)² – +...+ (–1)"+1 (x-3)²n + • - 2! 3! n! 50! What is the value of f (24) (3)? 1 24! 24! 12! 1 24! 24! 12! 1 12!
The Taylor series for a function f about x=2 is given by >n-0 (-1)“
п Зп+1
(x – 2)" which converges for 0<x<4. If the
2"
third-degree Taylor Polynomial for f about x=2 is used to approximate f
9
what is the alternating series error bound?
10
8.43
1
24-44
13-94
16-44
13
16-44
Transcribed Image Text:The Taylor series for a function f about x=2 is given by >n-0 (-1)“ п Зп+1 (x – 2)" which converges for 0<x<4. If the 2" third-degree Taylor Polynomial for f about x=2 is used to approximate f 9 what is the alternating series error bound? 10 8.43 1 24-44 13-94 16-44 13 16-44
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