The values of various roots can be approximated using Newton's method. For example, to approximate the value of √/10, let x =√10 and cube both sides of the equation to obtain x³ = 10, or x³ - 10 = 0. Therefore, 10 is a root of p(x)=x³ - 10, which can be approximated by applying Newton's method. Approximate the following value of r by first finding a polynomial with integer coefficients that has a root r. Use an appropriate value of x, and stop calculating approximations when two successive approximations agree to five digits to the right of the decimal point after rounding. r=(-12)3 (Type an integer or decimal rounded to five decimal places as needed.) 12
The values of various roots can be approximated using Newton's method. For example, to approximate the value of √/10, let x =√10 and cube both sides of the equation to obtain x³ = 10, or x³ - 10 = 0. Therefore, 10 is a root of p(x)=x³ - 10, which can be approximated by applying Newton's method. Approximate the following value of r by first finding a polynomial with integer coefficients that has a root r. Use an appropriate value of x, and stop calculating approximations when two successive approximations agree to five digits to the right of the decimal point after rounding. r=(-12)3 (Type an integer or decimal rounded to five decimal places as needed.) 12
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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
Transcribed Image Text:The values of various roots can be approximated using Newton's method. For example, to approximate the value of √/10, let x = ³/10 and cube both sides of the
equation to obtain x³ = 10, or x³ - 10 = 0. Therefore, 10 is a root of p(x) = x³-10, which can be approximated by applying Newton's method. Approximate the
following value of r by first finding a polynomial with integer coefficients that has a root r. Use an appropriate value of x and stop calculating approximations when
two successive approximations agree to five digits to the right of the decimal point after rounding.
r=(-12)³
(Type an integer or decimal rounded to five decimal places as needed.)
r≈
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