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Find the relative condition numbers of the follow- ing problems. Then identify all the values of x, if any, where the problem becomes poorly condi- tioned. (For instance, "x close to zero", "large |x|", etc. ) et – 1 (1) f(x) = 1- cos I (2) f(x) =

Find the relative condition numbers of the follow- ing problems. Then identify all the values of x, if any, where the problem becomes poorly condi- tioned. (For instance, "x close to zero", "large |x|", etc. ) et – 1 (1) f(x) = 1- cos I (2) f(x) =

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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Find the relative condition numbers of the follow- ing problems. Then identify all the values of x, if any, where the problem becomes poorly condi- tioned. (For instance, "x close to zero", "large |x|", etc. ) e – 1 (1) f(x) : 1- cos x (2) f(x) =
Transcribed Image Text:Find the relative condition numbers of the follow- ing problems. Then identify all the values of x, if any, where the problem becomes poorly condi- tioned. (For instance, "x close to zero", "large |x|", etc. ) e – 1 (1) f(x) : 1- cos x (2) f(x) =
Expert Solution
Step 1: Given.

Definition: For normed linear spaces X, ·X and Y, ·Y, nonempty open U in X, and f:U→Y, If f is differentiable at x∈U then the relative condition number of f at x∈U is,

κ(x)=Df(x)X, Yf(x)Y/xX.

Given: (1) f(x)=ex-1x

(2) f(x)=1-cosxx

 

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