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 xo and stop calculating approximations when two successive approximations agree to five digits to the right of the decimal point after rounding 1 r=5

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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The values of various roots can be approximated using Newton's method. For example, to approximate the value of
-10=0. Therefore, 10 is a root of
3
3
√10, let x = ³√10 and cube both sides of the equation to obtain x³ = 10, or
or x³_
3
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.
1
r≈
r = 5
3
(Type an integer or decimal rounded to five decimal places as needed.)
Transcribed Image Text:The values of various roots can be approximated using Newton's method. For example, to approximate the value of -10=0. Therefore, 10 is a root of 3 3 √10, let x = ³√10 and cube both sides of the equation to obtain x³ = 10, or or x³_ 3 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. 1 r≈ r = 5 3 (Type an integer or decimal rounded to five decimal places as needed.)
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