(a) Given an initial approximation x 1 to a root of the equation f ( x ) = 0, explain geometrically, with a diagram, how the second approximation x 2 in Newton’s method is obtained. (b) Write an expression for x 2 in terms of x 1 , f ( x 1 ), and f ′( x 1 ). (c) Write an expression for x n +1 in terms of x n , f ( x n ), and f ′( x n ). (d) Under what circumstances is Newton’s method likely to fail or to work very slowly?

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(a) Given an initial approximation x 1 to a root of the equation f ( x ) = 0, explain geometrically, with a diagram, how the second approximation x 2 in Newton’s method is obtained. (b) Write an expression for x 2 in terms of x 1 , f ( x 1 ), and f ′( x 1 ). (c) Write an expression for x n +1 in terms of x n , f ( x n ), and f ′( x n ). (d) Under what circumstances is Newton’s method likely to fail or to work very slowly?

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Question Text	(a) Given an initial approximation x 1 to a root of the equation f ( x ) = 0, explain geometrically, with a diagram, how the second approximation x 2 in Newton’s method is obtained. (b) Write an expression for x 2 in terms of x 1 , f ( x 1 ), and f ′( x 1 ). (c) Write an expression for x n +1 in terms of x n , f ( x n ), and f ′( x n ). (d) Under what circumstances is Newton’s method likely to fail or to work very slowly?
Topic	All Topics
Subject	Pre Calculus
Class	Class 11

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