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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,
Correct answer is between '1.53,1.59'. Can you explain this answer?
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Solve the equation x=10 cos(x) using the Newton-Raphson method. The in...
Let's start by finding the derivative of the equation:
f(x) = x - 10cos(x)
f'(x) = 1 + 10sin(x)
Now, let's use the Newton-Raphson method:
Step 1: Choose an initial guess, let's say x = 1.
Step 2: Use the formula x1 = x0 - f(x0)/f'(x0) to find the next approximation.
x1 = x0 - (x0 - 10cos(x0))/(1 + 10sin(x0))
Step 3: Repeat Step 2 until the desired accuracy is achieved.
Let's perform the calculations:
x1 = 1 - (1 - 10cos(1))/(1 + 10sin(1)) ≈ 1.291
x2 = 1.291 - (1.291 - 10cos(1.291))/(1 + 10sin(1.291)) ≈ 1.739
x3 = 1.739 - (1.739 - 10cos(1.739))/(1 + 10sin(1.739)) ≈ 1.865
x4 = 1.865 - (1.865 - 10cos(1.865))/(1 + 10sin(1.865)) ≈ 1.864
After repeating Step 2 a few more times, we find that x ≈ 1.864 is a solution to the equation x = 10cos(x) using the Newton-Raphson method with an initial guess of x = 1.
f(x) = x - 10cos(x)
f'(x) = 1 + 10sin(x)
Now, let's use the Newton-Raphson method:
Step 1: Choose an initial guess, let's say x = 1.
Step 2: Use the formula x1 = x0 - f(x0)/f'(x0) to find the next approximation.
x1 = x0 - (x0 - 10cos(x0))/(1 + 10sin(x0))
Step 3: Repeat Step 2 until the desired accuracy is achieved.
Let's perform the calculations:
x1 = 1 - (1 - 10cos(1))/(1 + 10sin(1)) ≈ 1.291
x2 = 1.291 - (1.291 - 10cos(1.291))/(1 + 10sin(1.291)) ≈ 1.739
x3 = 1.739 - (1.739 - 10cos(1.739))/(1 + 10sin(1.739)) ≈ 1.865
x4 = 1.865 - (1.865 - 10cos(1.865))/(1 + 10sin(1.865)) ≈ 1.864
After repeating Step 2 a few more times, we find that x ≈ 1.864 is a solution to the equation x = 10cos(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,Correct answer is between '1.53,1.59'. 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,Correct answer is between '1.53,1.59'. 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,Correct answer is between '1.53,1.59'. 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,Correct answer is between '1.53,1.59'. Can you explain this answer?.
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