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r = 10 1 5

r = 10 1 5

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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3 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 app priate value of xo and stop calculating approximations when two successive approximations agree to five digits to the right of the decimal point after rounding. 1 r = 105 ra (Type an integer or decimal rounded to five decimal places as needed.)
Transcribed Image Text:3 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 app priate value of xo and stop calculating approximations when two successive approximations agree to five digits to the right of the decimal point after rounding. 1 r = 105 ra (Type an integer or decimal rounded to five decimal places as needed.)
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