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Let P(x) be the fifth-degree Taylor polynomial for a function f about x=0. Information about the maximum absolute value of selected derivatives of f over the interval Osxs1.2 is given in the table below: 5) (x)| = 8.4 F() (x2)| = 411.8 58.8 max 0

Let P(x) be the fifth-degree Taylor polynomial for a function f about x=0. Information about the maximum absolute value of selected derivatives of f over the interval Osxs1.2 is given in the table below: 5) (x)| = 8.4 F() (x2)| = 411.8 58.8 max 0

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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Let P(x) be the fifth-degree Taylor polynomial for a function f about x=0. Information about the maximum absolute value of selected derivatives of f over the interval 0<xs1.2 is given in the table below: max f (x) = 8.4 0<x<1.2 (5) max 0<x<1.2 |F® (x) = 58.8 max f (x) = 411.8 0<x<1.2 If f(1.2) were approximated using P(1.2), what is the maximum error bound given by the Lagrange Remainder formula?
Transcribed Image Text:Let P(x) be the fifth-degree Taylor polynomial for a function f about x=0. Information about the maximum absolute value of selected derivatives of f over the interval 0<xs1.2 is given in the table below: max f (x) = 8.4 0<x<1.2 (5) max 0<x<1.2 |F® (x) = 58.8 max f (x) = 411.8 0<x<1.2 If f(1.2) were approximated using P(1.2), what is the maximum error bound given by the Lagrange Remainder formula?
If the series 1(-1)" 2 were approximated using its first k terms, what would be the smallest number for k such that the =1 n 3 ? alternating series error bound would guarantee an error of not more than 100 67
Transcribed Image Text:If the series 1(-1)" 2 were approximated using its first k terms, what would be the smallest number for k such that the =1 n 3 ? alternating series error bound would guarantee an error of not more than 100 67
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