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To solve the equation 2 sin x = x by Newton-Raphson method, the initial guess was chosen to be x = 2.0. Consider x in radian only. The value of x (in radian) obtained after one iteration will be closest to
- a)-8.101
- b)1.901
- c)2.099
- d)12.101
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
To solve the equation 2 sin x = x by Newton-Raphson method, the initia...
Concept:
The iterative formula for Newton Raphson method is given as,
[NOTE: Take the trignometric terms in Radian while using scitific calculator for this type of numericals]
Calculation:
Given:
f(x) = 2 sin x - x
∴ f'(x) = 2 cos x - 1
Initial guess is x0 = 2.0
The first iteration by Newton Raphson method is given by,
⇒ x1 = 1.901
The iterative formula for Newton Raphson method is given as,
[NOTE: Take the trignometric terms in Radian while using scitific calculator for this type of numericals]
Calculation:
Given:
f(x) = 2 sin x - x
∴ f'(x) = 2 cos x - 1
Initial guess is x0 = 2.0
The first iteration by Newton Raphson method is given by,
⇒ x1 = 1.901
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Community Answer
To solve the equation 2 sin x = x by Newton-Raphson method, the initia...
Initial Guess:
The equation given is 2 sin x = x. To solve this equation using the Newton-Raphson method, an initial guess of x = 2.0 is chosen.
Newton-Raphson Method:
The Newton-Raphson method is an iterative numerical technique used to find the roots of a real-valued function.
Iteration Process:
1. Calculate the value of the function f(x) = 2 sin(x) - x at the initial guess x = 2.0.
2. Calculate the derivative of the function f'(x) = 2 cos(x) - 1.
3. Update the value of x using the formula: x1 = x0 - f(x0)/f'(x0), where x0 is the initial guess.
4. Repeat steps 1-3 until convergence is achieved.
Calculation:
1. At x = 2.0, f(2.0) = 2 sin(2.0) - 2.0 ≈ -0.4161.
2. At x = 2.0, f'(2.0) = 2 cos(2.0) - 1 ≈ -1.8323.
3. Update x: x1 = 2.0 - (-0.4161)/(-1.8323) ≈ 1.9014.
Therefore, the value of x obtained after one iteration is closest to 1.901 radians, which corresponds to option B.
The equation given is 2 sin x = x. To solve this equation using the Newton-Raphson method, an initial guess of x = 2.0 is chosen.
Newton-Raphson Method:
The Newton-Raphson method is an iterative numerical technique used to find the roots of a real-valued function.
Iteration Process:
1. Calculate the value of the function f(x) = 2 sin(x) - x at the initial guess x = 2.0.
2. Calculate the derivative of the function f'(x) = 2 cos(x) - 1.
3. Update the value of x using the formula: x1 = x0 - f(x0)/f'(x0), where x0 is the initial guess.
4. Repeat steps 1-3 until convergence is achieved.
Calculation:
1. At x = 2.0, f(2.0) = 2 sin(2.0) - 2.0 ≈ -0.4161.
2. At x = 2.0, f'(2.0) = 2 cos(2.0) - 1 ≈ -1.8323.
3. Update x: x1 = 2.0 - (-0.4161)/(-1.8323) ≈ 1.9014.
Therefore, the value of x obtained after one iteration is closest to 1.901 radians, which corresponds to option B.
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To solve the equation 2 sin x = x by Newton-Raphson method, the initial guess was chosen to be x = 2.0. Consider x in radian only. The value of x (in radian) obtained after one iteration will be closest toa)-8.101b)1.901c)2.099d)12.101Correct answer is option 'B'. Can you explain this answer?
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