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Solve the equation x = 10 cos (x) using the Newton-Raphson method. The initial guess is x = π/4.
The value of the predicted root after the first iteration, up to second decimal, is __________.
The value of the predicted root after the first iteration, up to second decimal, is __________.
(Important - Enter only the numerical value in the answer)
Correct answer is '1.5641'. Can you explain this answer?
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Solve the equation x = 10 cos (x) using the Newton-Raphson method. The...
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Solve the equation x = 10 cos (x) using the Newton-Raphson method. The...
Let's use the Newton-Raphson method to solve the equation x = 10 cos(x) with an initial guess of x = 1.
The first step is to find the derivative of the function f(x) = x - 10cos(x). The derivative is f'(x) = 1 + 10sin(x).
Next, we can use the following iteration formula to update our guess:
x_new = x - f(x)/f'(x)
Using x = 1 as our initial guess, we can calculate the updated guess as follows:
x_new = 1 - (1 - 10cos(1))/(1 + 10sin(1)) ≈ 0.7390851
Now we can repeat the process using x_new as our new guess:
x_new = 0.7390851 - (0.7390851 - 10cos(0.7390851))/(1 + 10sin(0.7390851)) ≈ 0.7390851
We can see that the updated guess is approximately the same as the previous one. This suggests that we have found the solution to the equation.
Therefore, x ≈ 0.7390851 is the solution to the equation x = 10 cos(x) using the Newton-Raphson method with an initial guess of x = 1.
The first step is to find the derivative of the function f(x) = x - 10cos(x). The derivative is f'(x) = 1 + 10sin(x).
Next, we can use the following iteration formula to update our guess:
x_new = x - f(x)/f'(x)
Using x = 1 as our initial guess, we can calculate the updated guess as follows:
x_new = 1 - (1 - 10cos(1))/(1 + 10sin(1)) ≈ 0.7390851
Now we can repeat the process using x_new as our new guess:
x_new = 0.7390851 - (0.7390851 - 10cos(0.7390851))/(1 + 10sin(0.7390851)) ≈ 0.7390851
We can see that the updated guess is approximately the same as the previous one. This suggests that we have found the solution to the equation.
Therefore, x ≈ 0.7390851 is the solution to the equation x = 10 cos(x) using the Newton-Raphson method with an initial guess of x = 1.
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Solve the equation x = 10 cos (x) using the Newton-Raphson method. The initial guess is x = π/4.The value of the predicted root after the first iteration, up to second decimal, is __________.(Important - Enter only the numerical value in the answer)Correct answer is '1.5641'. Can you explain this answer?
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Solve the equation x = 10 cos (x) using the Newton-Raphson method. The initial guess is x = π/4.The value of the predicted root after the first iteration, up to second decimal, is __________.(Important - Enter only the numerical value in the answer)Correct answer is '1.5641'. 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 Solve the equation x = 10 cos (x) using the Newton-Raphson method. The initial guess is x = π/4.The value of the predicted root after the first iteration, up to second decimal, is __________.(Important - Enter only the numerical value in the answer)Correct answer is '1.5641'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the equation x = 10 cos (x) using the Newton-Raphson method. The initial guess is x = π/4.The value of the predicted root after the first iteration, up to second decimal, is __________.(Important - Enter only the numerical value in the answer)Correct answer is '1.5641'. Can you explain this answer?.
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