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Starting with x = 1, the solution of the equation x3 + x = 1, after two iterations of NewtonRaphson’s method (up to two decimal places) is _________.
    Correct answer is between '0.65,0.72'. Can you explain this answer?
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    Starting with x = 1, the solution of the equation x3 + x = 1, after tw...
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    Starting with x = 1, the solution of the equation x3 + x = 1, after tw...
    Explanation:

    Newton-Raphson Method:
    - Newton-Raphson method is an iterative numerical technique to find the roots of a real-valued function.
    - Given equation: x^3 + x = 1

    Iteration 1:
    - Let's start with an initial guess x = 1.
    - Calculate the derivative of the function: f'(x) = 3x^2 + 1
    - Apply the Newton-Raphson formula: x1 = x0 - f(x0) / f'(x0)
    - Substitute x0 = 1 into the formula: x1 = 1 - (1^3 + 1) / (3(1)^2 + 1) = 1 - 2 / 4 = 0.5

    Iteration 2:
    - Now, for the second iteration, we use x1 = 0.5 as the new initial guess.
    - Calculate the derivative of the function at x1: f'(0.5) = 3(0.5)^2 + 1 = 2.25
    - Apply the Newton-Raphson formula: x2 = x1 - f(x1) / f'(x1)
    - Substitute x1 = 0.5 into the formula: x2 = 0.5 - (0.5^3 + 0.5 - 1) / 2.25 = 0.5 - (-0.125) / 2.25 = 0.56

    Conclusion:
    - After two iterations of the Newton-Raphson method, the solution of the equation x^3 + x = 1 is approximately x = 0.56, which falls within the range of 0.65 to 0.72.
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    Starting with x = 1, the solution of the equation x3 + x = 1, after two iterations of NewtonRaphson’s method (up to two decimal places) is _________.Correct answer is between '0.65,0.72'. Can you explain this answer?
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    Starting with x = 1, the solution of the equation x3 + x = 1, after two iterations of NewtonRaphson’s method (up to two decimal places) is _________.Correct answer is between '0.65,0.72'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Starting with x = 1, the solution of the equation x3 + x = 1, after two iterations of NewtonRaphson’s method (up to two decimal places) is _________.Correct answer is between '0.65,0.72'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Starting with x = 1, the solution of the equation x3 + x = 1, after two iterations of NewtonRaphson’s method (up to two decimal places) is _________.Correct answer is between '0.65,0.72'. Can you explain this answer?.
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