2. Let f(x) = 3√x. (a) Find the absolute and relative condition numbers of f. (b) Where is f well conditioned in an absolute sense? In a relative sense? (c) Suppose x = 10-17 is replaced by x = 10-16 (a small absolute change but a large relative change). Using the absolute condition number of f, how much of a change is expected in f due to this change in the argument?
2. Let f(x) = 3√x. (a) Find the absolute and relative condition numbers of f. (b) Where is f well conditioned in an absolute sense? In a relative sense? (c) Suppose x = 10-17 is replaced by x = 10-16 (a small absolute change but a large relative change). Using the absolute condition number of f, how much of a change is expected in f due to this change in the argument?
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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Please answer parts b and c
Transcribed Image Text:2. Let f(x) = 3√x.
(a) Find the absolute and relative condition numbers of f.
(b) Where is f well conditioned in an absolute sense? In a relative sense?
(c) Suppose x = 10-17 is replaced by x = 10-16 (a small absolute change
but a large relative change). Using the absolute condition number of f,
how much of a change is expected in f due to this change in the
argument?
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