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The second approximation for the root of the equation 3x = cosx + 1 between 0 and 1 with X0 = 0.6 by Newton Raphson method is:
- a)0.607
- b)0.517
- c)0.606
- d)0.350
Correct answer is option 'A'. Can you explain this answer?
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Newton Raphson Method for Finding Roots
The Newton Raphson method is an iterative method to find the roots of an equation. It starts with an initial guess and then improves the guess in each iteration until a satisfactory accuracy is achieved.
Algorithm:
1. Choose an initial guess x0
2. Calculate f(x0) and f'(x0)
3. Calculate the next approximation using the formula: xn+1 = xn - f(xn)/f'(xn)
4. Repeat steps 2 and 3 until the desired accuracy is achieved
Applying Newton Raphson Method to the given equation
Given equation: 3x = cosx - 1
Let f(x) = 3x - cosx + 1
We need to find the root of f(x) between 0 and 1 with X0 = 0.6
Step 1: Choose an initial guess x0 = 0.6
Step 2: Calculate f(x0) and f'(x0)
f(x0) = 3(0.6) - cos(0.6) + 1 = 0.077
f'(x0) = 3 + sin(0.6) ≈ 3.5
Step 3: Calculate the next approximation using the formula: xn+1 = xn - f(xn)/f'(xn)
x1 = 0.6 - 0.077/3.5 ≈ 0.582
Step 4: Repeat steps 2 and 3 until the desired accuracy is achieved
x2 = x1 - f(x1)/f'(x1) ≈ 0.607
Therefore, the second approximation for the root of the equation 3x = cosx - 1 between 0 and 1 with X0 = 0.6 by Newton Raphson method is 0.607, which is option A.
The Newton Raphson method is an iterative method to find the roots of an equation. It starts with an initial guess and then improves the guess in each iteration until a satisfactory accuracy is achieved.
Algorithm:
1. Choose an initial guess x0
2. Calculate f(x0) and f'(x0)
3. Calculate the next approximation using the formula: xn+1 = xn - f(xn)/f'(xn)
4. Repeat steps 2 and 3 until the desired accuracy is achieved
Applying Newton Raphson Method to the given equation
Given equation: 3x = cosx - 1
Let f(x) = 3x - cosx + 1
We need to find the root of f(x) between 0 and 1 with X0 = 0.6
Step 1: Choose an initial guess x0 = 0.6
Step 2: Calculate f(x0) and f'(x0)
f(x0) = 3(0.6) - cos(0.6) + 1 = 0.077
f'(x0) = 3 + sin(0.6) ≈ 3.5
Step 3: Calculate the next approximation using the formula: xn+1 = xn - f(xn)/f'(xn)
x1 = 0.6 - 0.077/3.5 ≈ 0.582
Step 4: Repeat steps 2 and 3 until the desired accuracy is achieved
x2 = x1 - f(x1)/f'(x1) ≈ 0.607
Therefore, the second approximation for the root of the equation 3x = cosx - 1 between 0 and 1 with X0 = 0.6 by Newton Raphson method is 0.607, which is option A.
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The second approximation for the root of the equation 3x = cosx + 1 between 0 and 1 with X0 = 0.6 by Newton Raphson method is:a)0.607b)0.517c)0.606d)0.350Correct answer is option 'A'. Can you explain this answer?
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The second approximation for the root of the equation 3x = cosx + 1 between 0 and 1 with X0 = 0.6 by Newton Raphson method is:a)0.607b)0.517c)0.606d)0.350Correct answer is option 'A'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about The second approximation for the root of the equation 3x = cosx + 1 between 0 and 1 with X0 = 0.6 by Newton Raphson method is:a)0.607b)0.517c)0.606d)0.350Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The second approximation for the root of the equation 3x = cosx + 1 between 0 and 1 with X0 = 0.6 by Newton Raphson method is:a)0.607b)0.517c)0.606d)0.350Correct answer is option 'A'. Can you explain this answer?.
The second approximation for the root of the equation 3x = cosx + 1 between 0 and 1 with X0 = 0.6 by Newton Raphson method is:a)0.607b)0.517c)0.606d)0.350Correct answer is option 'A'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about The second approximation for the root of the equation 3x = cosx + 1 between 0 and 1 with X0 = 0.6 by Newton Raphson method is:a)0.607b)0.517c)0.606d)0.350Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The second approximation for the root of the equation 3x = cosx + 1 between 0 and 1 with X0 = 0.6 by Newton Raphson method is:a)0.607b)0.517c)0.606d)0.350Correct answer is option 'A'. Can you explain this answer?.
Solutions for The second approximation for the root of the equation 3x = cosx + 1 between 0 and 1 with X0 = 0.6 by Newton Raphson method is:a)0.607b)0.517c)0.606d)0.350Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for SSC.
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