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Newton raphson method is to be used to find root of equation 3x – ex + sinx = 0. If the initial trial value of the roots is taken as 0.333, the next approximation for the root would be
- a)0.49
- b)0.68
- c)0.25
- d)0.36
Correct answer is option 'D'. Can you explain this answer?
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Newton raphson method is to be used to find root of equation 3x &ndash...
The Newton-Raphson method is an iterative numerical method used to find the roots of a given equation. To use this method to find the root of the equation 3x, we need to rewrite it in the form f(x) = 0.
The equation 3x can be rewritten as f(x) = 3x - 0. To find the root of this equation using the Newton-Raphson method, we follow these steps:
1. Start with an initial guess for the root, let's call it x₀.
2. Calculate the function value at the initial guess, f(x₀) = 3x₀ - 0.
3. Calculate the derivative of the function, f'(x) = 3.
4. Use the formula x₁ = x₀ - f(x₀)/f'(x₀) to find the next approximation of the root.
5. Repeat steps 2 to 4 until the desired level of accuracy is achieved or until the algorithm converges.
Here is the general formula for the Newton-Raphson method:
x₁ = x₀ - f(x₀)/f'(x₀)
Note that the derivative of the equation 3x is constant and equal to 3, so the formula simplifies to:
x₁ = x₀ - (3x₀ - 0)/3
Simplifying further:
x₁ = x₀ - x₀/3
This can be rewritten as:
x₁ = (2/3)x₀
By repeating this process, we can iterate to find better approximations of the root.
The equation 3x can be rewritten as f(x) = 3x - 0. To find the root of this equation using the Newton-Raphson method, we follow these steps:
1. Start with an initial guess for the root, let's call it x₀.
2. Calculate the function value at the initial guess, f(x₀) = 3x₀ - 0.
3. Calculate the derivative of the function, f'(x) = 3.
4. Use the formula x₁ = x₀ - f(x₀)/f'(x₀) to find the next approximation of the root.
5. Repeat steps 2 to 4 until the desired level of accuracy is achieved or until the algorithm converges.
Here is the general formula for the Newton-Raphson method:
x₁ = x₀ - f(x₀)/f'(x₀)
Note that the derivative of the equation 3x is constant and equal to 3, so the formula simplifies to:
x₁ = x₀ - (3x₀ - 0)/3
Simplifying further:
x₁ = x₀ - x₀/3
This can be rewritten as:
x₁ = (2/3)x₀
By repeating this process, we can iterate to find better approximations of the root.
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Newton raphson method is to be used to find root of equation 3x – ex + sinx = 0. If the initial trial value of the roots is taken as 0.333, the next approximation for the root would bea)0.49b)0.68c)0.25d)0.36Correct answer is option 'D'. Can you explain this answer?
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Newton raphson method is to be used to find root of equation 3x – ex + sinx = 0. If the initial trial value of the roots is taken as 0.333, the next approximation for the root would bea)0.49b)0.68c)0.25d)0.36Correct answer is option 'D'. 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 Newton raphson method is to be used to find root of equation 3x – ex + sinx = 0. If the initial trial value of the roots is taken as 0.333, the next approximation for the root would bea)0.49b)0.68c)0.25d)0.36Correct answer is option 'D'. 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 Newton raphson method is to be used to find root of equation 3x – ex + sinx = 0. If the initial trial value of the roots is taken as 0.333, the next approximation for the root would bea)0.49b)0.68c)0.25d)0.36Correct answer is option 'D'. Can you explain this answer?.
Newton raphson method is to be used to find root of equation 3x – ex + sinx = 0. If the initial trial value of the roots is taken as 0.333, the next approximation for the root would bea)0.49b)0.68c)0.25d)0.36Correct answer is option 'D'. 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 Newton raphson method is to be used to find root of equation 3x – ex + sinx = 0. If the initial trial value of the roots is taken as 0.333, the next approximation for the root would bea)0.49b)0.68c)0.25d)0.36Correct answer is option 'D'. 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 Newton raphson method is to be used to find root of equation 3x – ex + sinx = 0. If the initial trial value of the roots is taken as 0.333, the next approximation for the root would bea)0.49b)0.68c)0.25d)0.36Correct answer is option 'D'. Can you explain this answer?.
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