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Newton-Raphson method is to be used to find root of equation 3x - ex + sinx = 0. If the initial trial value for the root is taken as 0.333, the next approximation for the root would be ______________.
(Answer up to two decimal places)
Correct answer is '0.36'. Can you explain this answer?
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Newton-Raphson method is to be used to find root of equation 3x - ex ...
Newton-Raphson Method to Find Root of Equation
The Newton-Raphson method is an iterative technique used to find the root of a function. It is a powerful numerical method for solving nonlinear equations. Here is how it works:
1. Start with an initial guess for the root.
2. Calculate the function and its derivative at that point.
3. Use these values to find the next approximation for the root.
4. Repeat steps 2 and 3 until the desired accuracy is achieved.
Given Equation and Initial Trial Value
The equation to be solved using the Newton-Raphson method is:
3x - ex sinx = 0
The initial trial value for the root is taken as 0.333.
Finding the Next Approximation for the Root
To find the next approximation for the root using the Newton-Raphson method, we need to calculate the function and its derivative at the initial trial value.
f(x) = 3x - ex sinx
f'(x) = 3 - ex cosx - ex sinx
At x = 0.333, we have:
f(0.333) = 3(0.333) - e(0.333) sin(0.333) = -0.051
f'(0.333) = 3 - e(0.333) cos(0.333) - e(0.333) sin(0.333) = 2.300
Using these values, we can find the next approximation for the root:
x1 = x0 - f(x0)/f'(x0)
where x0 is the initial trial value and x1 is the next approximation for the root.
Substituting the values, we get:
x1 = 0.333 - (-0.051)/2.300 = 0.36 (rounded to two decimal places)
Therefore, the next approximation for the root is 0.36. We can continue this process until we reach the desired level of accuracy.
The Newton-Raphson method is an iterative technique used to find the root of a function. It is a powerful numerical method for solving nonlinear equations. Here is how it works:
1. Start with an initial guess for the root.
2. Calculate the function and its derivative at that point.
3. Use these values to find the next approximation for the root.
4. Repeat steps 2 and 3 until the desired accuracy is achieved.
Given Equation and Initial Trial Value
The equation to be solved using the Newton-Raphson method is:
3x - ex sinx = 0
The initial trial value for the root is taken as 0.333.
Finding the Next Approximation for the Root
To find the next approximation for the root using the Newton-Raphson method, we need to calculate the function and its derivative at the initial trial value.
f(x) = 3x - ex sinx
f'(x) = 3 - ex cosx - ex sinx
At x = 0.333, we have:
f(0.333) = 3(0.333) - e(0.333) sin(0.333) = -0.051
f'(0.333) = 3 - e(0.333) cos(0.333) - e(0.333) sin(0.333) = 2.300
Using these values, we can find the next approximation for the root:
x1 = x0 - f(x0)/f'(x0)
where x0 is the initial trial value and x1 is the next approximation for the root.
Substituting the values, we get:
x1 = 0.333 - (-0.051)/2.300 = 0.36 (rounded to two decimal places)
Therefore, the next approximation for the root is 0.36. We can continue this process until we reach the desired level of accuracy.
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Community Answer
Newton-Raphson method is to be used to find root of equation 3x - ex ...
Let f(x) = 3x - ex + sinx and x0 = 0.333 ≈ 1/3
⇒ f'(x) = 3 - ex + cos x
f(x0) = -0.069 and f'(x0) = 2.55
∴ x1 = x0 - [f(xo)]/[f’(x0)] (Using Newton-Rapshon method)
= 0.333 + 0.069/2.55 = 0.36 is the required next approximation
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Newton-Raphson method is to be used to find root of equation 3x - ex + sinx = 0. If the initial trial value for the root is taken as 0.333, the next approximation for the root would be ______________.(Answer up to two decimal places)Correct answer is '0.36'. Can you explain this answer?
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Newton-Raphson method is to be used to find root of equation 3x - ex + sinx = 0. If the initial trial value for the root is taken as 0.333, the next approximation for the root would be ______________.(Answer up to two decimal places)Correct answer is '0.36'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Newton-Raphson method is to be used to find root of equation 3x - ex + sinx = 0. If the initial trial value for the root is taken as 0.333, the next approximation for the root would be ______________.(Answer up to two decimal places)Correct answer is '0.36'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Newton-Raphson method is to be used to find root of equation 3x - ex + sinx = 0. If the initial trial value for the root is taken as 0.333, the next approximation for the root would be ______________.(Answer up to two decimal places)Correct answer is '0.36'. Can you explain this answer?.
Newton-Raphson method is to be used to find root of equation 3x - ex + sinx = 0. If the initial trial value for the root is taken as 0.333, the next approximation for the root would be ______________.(Answer up to two decimal places)Correct answer is '0.36'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Newton-Raphson method is to be used to find root of equation 3x - ex + sinx = 0. If the initial trial value for the root is taken as 0.333, the next approximation for the root would be ______________.(Answer up to two decimal places)Correct answer is '0.36'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Newton-Raphson method is to be used to find root of equation 3x - ex + sinx = 0. If the initial trial value for the root is taken as 0.333, the next approximation for the root would be ______________.(Answer up to two decimal places)Correct answer is '0.36'. Can you explain this answer?.
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