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The square root of a number N is to be obtained by applying the Newton Raphson iterations to the equation x2 - N = 0, if i denotes the iteration index, the correct iterative scheme will be
  • a)
    xi+1 = (xi + N/xi)/2
  • b)
    xi+1 = (x2i + N/x2i)/2
  • c)
    xi+1 = (xi + N2/xi)/2
  • d)
    xi+1 = (xi - N/xi)/2
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The square root of a number N is to be obtained by applying the Newton...
Given
Now,
f(x) = x2 – N = 0
Differentiating,
f’(x) = 2x
Now,
Using Newton-Raphson Method,

xi+1 = (xi + N/xi)/2
Free Test
Community Answer
The square root of a number N is to be obtained by applying the Newton...
Explanation:

Newton Raphson Iterations:
- Newton Raphson iterations are used to approximate the roots of a real-valued function.
- In this case, the function is x^2 - N = 0, where N is the number whose square root we want to find.

Iterative Scheme:
- The correct iterative scheme for finding the square root of N using Newton Raphson iterations is given by the formula:
- xi+1 = (xi + N/xi)/2

Explanation of the Iterative Scheme:
- In each iteration, xi is the current approximation of the square root of N.
- To improve the approximation, we calculate xi+1 using the formula above.
- This formula is derived from the Newton Raphson method for finding the roots of a function.

Choosing the Correct Option:
- Option 'A' matches the correct iterative scheme for finding the square root of N using Newton Raphson iterations.
- The other options do not match the correct formula for the iterative scheme.

Conclusion:
- The correct option for the iterative scheme to find the square root of a number N using Newton Raphson iterations is option 'A'.
- By applying the formula xi+1 = (xi + N/xi)/2 iteratively, we can approximate the square root of N.
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The square root of a number N is to be obtained by applying the Newton Raphson iterations to the equation x2 - N = 0, if i denotes the iteration index, the correct iterative scheme will bea)xi+1 = (xi + N/xi)/2b)xi+1 = (x2i + N/x2i)/2c)xi+1 = (xi + N2/xi)/2d)xi+1 = (xi - N/xi)/2Correct answer is option 'A'. Can you explain this answer?
Question Description
The square root of a number N is to be obtained by applying the Newton Raphson iterations to the equation x2 - N = 0, if i denotes the iteration index, the correct iterative scheme will bea)xi+1 = (xi + N/xi)/2b)xi+1 = (x2i + N/x2i)/2c)xi+1 = (xi + N2/xi)/2d)xi+1 = (xi - N/xi)/2Correct answer is option 'A'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The square root of a number N is to be obtained by applying the Newton Raphson iterations to the equation x2 - N = 0, if i denotes the iteration index, the correct iterative scheme will bea)xi+1 = (xi + N/xi)/2b)xi+1 = (x2i + N/x2i)/2c)xi+1 = (xi + N2/xi)/2d)xi+1 = (xi - N/xi)/2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The square root of a number N is to be obtained by applying the Newton Raphson iterations to the equation x2 - N = 0, if i denotes the iteration index, the correct iterative scheme will bea)xi+1 = (xi + N/xi)/2b)xi+1 = (x2i + N/x2i)/2c)xi+1 = (xi + N2/xi)/2d)xi+1 = (xi - N/xi)/2Correct answer is option 'A'. Can you explain this answer?.
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