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Consider the following equation: 2 + cos(e* – 2) – ex = 0. A numerical algorithm produced the following approximation of a root r of this equation X, 1.00767372. How much is the backward error (give the answer with one significant digit) ? Estimate the multiplicity of the root the algorithm is trying to approximate : Estimate the absolute error |r – x,| of x, to one significant digit : How many correct significant digits contains x, ?

Consider the following equation: 2 + cos(e* – 2) – ex = 0. A numerical algorithm produced the following approximation of a root r of this equation X, 1.00767372. How much is the backward error (give the answer with one significant digit) ? Estimate the multiplicity of the root the algorithm is trying to approximate : Estimate the absolute error |r – x,| of x, to one significant digit : How many correct significant digits contains 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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Consider the following equation: 2 + cos(e* – 2) – ex = 0. A numerical algorithm produced the following approximation of a root r of this equation X, 1.00767372. How much is the backward error (give the answer with one significant digit) ? Estimate the multiplicity of the root the algorithm is trying to approximate : Estimate the absolute error |r – x,| of x, to one significant digit : How many correct significant digits contains x, ?
Transcribed Image Text:Consider the following equation: 2 + cos(e* – 2) – ex = 0. A numerical algorithm produced the following approximation of a root r of this equation X, 1.00767372. How much is the backward error (give the answer with one significant digit) ? Estimate the multiplicity of the root the algorithm is trying to approximate : Estimate the absolute error |r – x,| of x, to one significant digit : How many correct significant digits contains x, ?
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