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Home Limits, Analytic Geometry, and Approximations Newton's Method Examples Example 2: Approximating a Fifth Root  
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Example 2: Approximating a Fifth Root
Approximate the fifth root of 6 by Newton's method.
As a check we compute (x_{3})^{5} ~ 6.001 In this example more iterations would be necessary if our first approximation had not been chosen as well. For instance, starting with x_{1} = 1 we would not reach the approximation 1.431 until x_{6}, obtaining the successive approximations x_{1} = 1, x_{2} = 2, x_{3} = 1.675, x_{4} = 1.49245, x_{5} = 1.43583, x_{6} = 1.43100. Figure 5.9.5


Home Limits, Analytic Geometry, and Approximations Newton's Method Examples Example 2: Approximating a Fifth Root 