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39–42. Estimating roots The values of various roots can be ap- proximated using Newton's method. For example, to approximate the value of V10, we let x = V10 and cube both sides of the equation to obtain x = 10, or x³ – 10 = 0. Therefore, V10 is a root of p(x) = x – 10, which we can approximate by applying Newton's method. Approximate each 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 = (-9)/3

39–42. Estimating roots The values of various roots can be ap- proximated using Newton's method. For example, to approximate the value of V10, we let x = V10 and cube both sides of the equation to obtain x = 10, or x³ – 10 = 0. Therefore, V10 is a root of p(x) = x – 10, which we can approximate by applying Newton's method. Approximate each 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 = (-9)/3

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.5: Properties Of Logarithms
Problem 62E
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39–42. Estimating roots The values of various roots can be ap- proximated using Newton's method. For example, to approximate the value of V10, we let x = V10 and cube both sides of the equation to obtain x = 10, or x³ – 10 = 0. Therefore, V10 is a root of p(x) = x – 10, which we can approximate by applying Newton's method. Approximate each 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 = (-9)/3
Transcribed Image Text:39–42. Estimating roots The values of various roots can be ap- proximated using Newton's method. For example, to approximate the value of V10, we let x = V10 and cube both sides of the equation to obtain x = 10, or x³ – 10 = 0. Therefore, V10 is a root of p(x) = x – 10, which we can approximate by applying Newton's method. Approximate each 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 = (-9)/3
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