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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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