`x/(x^2 + 1) = sqrt(1 - x)` Use Newton's method to find all roots of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations.

Textbook Question

Chapter 4, 4.8 - Problem 25 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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See the attached graph. From the graph the curve intersects x-axis at `~~` 0.8


Now x_1 `~~` 0.8



approximate until eight decimal places are same




To eight decimal places the root of the equation is `~~` 0.76682579

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