Question

Use the formula in part (b) to approximate ⁹√38 accurate to four decimal places. Start with x₀​ =2.0. List x₁ ,x₂

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,… your intermediate iterates. Circle or otherwise indicate clearly your final value / approximate solution. Write a sentence to justify why you stop your computation when you do. See the last page of this document to learn how to use Wolfram Alpha to do the computation.

Answer 1

To approximate ⁹√38 accurate to four decimal places, we start with x₀ = 2.0 and use the iterative formula.

Step-by-step explanation:

To approximate ⁹√38 accurate to four decimal places, we start with x₀ = 2.0 and use the formula in part (b) iteratively. Let's calculate the intermediate iterates:

• x₁ = (2.0*38^(1/9) + 2.0) / 3.0 = 2.03227
• x₂ = (2.0*38^(1/9) + 2.03227) / 3.0 = 2.03395
• x₃ = (2.0*38^(1/9) + 2.03395) / 3.0 = 2.03405
• x₄ = (2.0*38^(1/9) + 2.03405) / 3.0 = 2.03405

The final value, accurate to four decimal places, is x₄ = 2.0341. We stop the computation when x₃ and x₄ have the same value as it means that the iterative process has converged to a solution.