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The root of the function f(x) = x3 + x – 1 obtained after first iteration on application of newton raphson scheme using an initial guess of xo = 1 is
  • a)
    0.682
  • b)
    0.686
  • c)
    0.750
  • d)
    1.000
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The root of the function f(x) = x3 + x – 1 obtained after first ...
Newton-Raphson Method Iteration
Newton-Raphson method is an iterative numerical technique used for finding the roots of a real-valued function.

Given Function
f(x) = x^3 + x - 1

Initial Guess
xo = 1

Derivative of the Function
f'(x) = 3x^2 + 1

Newton-Raphson Formula
xo+1 = xo - f(xo) / f'(xo)

Calculation
- Calculate the value of the function at xo:
f(1) = 1^3 + 1 - 1 = 1
- Calculate the value of the derivative of the function at xo:
f'(1) = 3(1)^2 + 1 = 4
- Apply the Newton-Raphson formula to find the next approximation:
x1 = 1 - 1 / 4 = 0.75
Therefore, the root of the function f(x) = x^3 + x - 1 obtained after the first iteration using an initial guess of xo = 1 is 0.750. Hence, the correct answer is option C.
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The root of the function f(x) = x3 + x – 1 obtained after first iteration on application of newton raphson scheme using an initial guess of xo = 1 isa)0.682b)0.686c)0.750d)1.000Correct answer is option 'C'. Can you explain this answer?
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The root of the function f(x) = x3 + x – 1 obtained after first iteration on application of newton raphson scheme using an initial guess of xo = 1 isa)0.682b)0.686c)0.750d)1.000Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The root of the function f(x) = x3 + x – 1 obtained after first iteration on application of newton raphson scheme using an initial guess of xo = 1 isa)0.682b)0.686c)0.750d)1.000Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The root of the function f(x) = x3 + x – 1 obtained after first iteration on application of newton raphson scheme using an initial guess of xo = 1 isa)0.682b)0.686c)0.750d)1.000Correct answer is option 'C'. Can you explain this answer?.
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