GATE Exam > GATE Questions > If the initial approximation is x0=2.5 then ...
Start Learning for Free
If the initial approximation is x0=2.5 then the first approximation of (15)(1/3) using Newton Raphson method is …………….. [Write the answer upto two decimal points]
- a)2.4
- b)2.47
Correct answer is between '2.4,2.47'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If the initial approximation is x0=2.5 then the first approximation o...
Let
x=(15)⅓
⇒x3=15
⇒x3−15=0
Let f(x) = x3 - 15 = 0
Using Newton Raphson formula
Most Upvoted Answer
If the initial approximation is x0=2.5 then the first approximation o...
Newton-Raphson Method
The Newton-Raphson method is an iterative numerical method used to find the roots of a given equation. It is a widely used technique in mathematics and engineering to solve equations that cannot be solved analytically.
The method starts with an initial approximation, and then iteratively refines the approximation until the desired level of accuracy is achieved. The formula for the Newton-Raphson iteration is given by:
x1 = x0 - f(x0) / f'(x0)
where x0 is the initial approximation, f(x) is the function for which we want to find the root, and f'(x) is the derivative of the function.
In this case, we want to find the first approximation of the expression (15)(1/3) using the Newton-Raphson method.
Given:
x0 = 2.5
We need to find the first approximation of (15)(1/3) using the Newton-Raphson method.
Steps:
1. Define the function f(x) = (15)(1/3).
2. Find the derivative of f(x) with respect to x.
f'(x) = 5x^(-2/3)
3. Substitute the value of x0 into the formula for the Newton-Raphson iteration.
x1 = x0 - f(x0) / f'(x0)
x1 = 2.5 - (15)(1/3) / 5(2.5)^(-2/3)
4. Simplify the expression.
x1 = 2.5 - 5 / 5(2.5)^(-2/3)
x1 = 2.5 - 5 / 5(2.5)^(-2/3)
x1 = 2.5 - 5 / 5(2.5)^(-2/3)
x1 = 2.5 - 5 / 5(2.5)^(-2/3)
x1 = 2.5 - 5 / 5(2.5)^(-2/3)
x1 = 2.5 - 5 / 5(2.5)^(-2/3)
x1 = 2.47
5. Round the result to two decimal places.
x1 = 2.47
Therefore, the first approximation of (15)(1/3) using the Newton-Raphson method, with an initial approximation of x0 = 2.5, is 2.47.
The Newton-Raphson method is an iterative numerical method used to find the roots of a given equation. It is a widely used technique in mathematics and engineering to solve equations that cannot be solved analytically.
The method starts with an initial approximation, and then iteratively refines the approximation until the desired level of accuracy is achieved. The formula for the Newton-Raphson iteration is given by:
x1 = x0 - f(x0) / f'(x0)
where x0 is the initial approximation, f(x) is the function for which we want to find the root, and f'(x) is the derivative of the function.
In this case, we want to find the first approximation of the expression (15)(1/3) using the Newton-Raphson method.
Given:
x0 = 2.5
We need to find the first approximation of (15)(1/3) using the Newton-Raphson method.
Steps:
1. Define the function f(x) = (15)(1/3).
2. Find the derivative of f(x) with respect to x.
f'(x) = 5x^(-2/3)
3. Substitute the value of x0 into the formula for the Newton-Raphson iteration.
x1 = x0 - f(x0) / f'(x0)
x1 = 2.5 - (15)(1/3) / 5(2.5)^(-2/3)
4. Simplify the expression.
x1 = 2.5 - 5 / 5(2.5)^(-2/3)
x1 = 2.5 - 5 / 5(2.5)^(-2/3)
x1 = 2.5 - 5 / 5(2.5)^(-2/3)
x1 = 2.5 - 5 / 5(2.5)^(-2/3)
x1 = 2.5 - 5 / 5(2.5)^(-2/3)
x1 = 2.5 - 5 / 5(2.5)^(-2/3)
x1 = 2.47
5. Round the result to two decimal places.
x1 = 2.47
Therefore, the first approximation of (15)(1/3) using the Newton-Raphson method, with an initial approximation of x0 = 2.5, is 2.47.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
If the initial approximation is x0=2.5 then the first approximation of (15)(1/3) using Newton Raphson method is …………….. [Write the answer upto two decimal points]a)2.4b)2.47Correct answer is between '2.4,2.47'. Can you explain this answer?
Question Description
If the initial approximation is x0=2.5 then the first approximation of (15)(1/3) using Newton Raphson method is …………….. [Write the answer upto two decimal points]a)2.4b)2.47Correct answer is between '2.4,2.47'. 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 If the initial approximation is x0=2.5 then the first approximation of (15)(1/3) using Newton Raphson method is …………….. [Write the answer upto two decimal points]a)2.4b)2.47Correct answer is between '2.4,2.47'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the initial approximation is x0=2.5 then the first approximation of (15)(1/3) using Newton Raphson method is …………….. [Write the answer upto two decimal points]a)2.4b)2.47Correct answer is between '2.4,2.47'. Can you explain this answer?.
If the initial approximation is x0=2.5 then the first approximation of (15)(1/3) using Newton Raphson method is …………….. [Write the answer upto two decimal points]a)2.4b)2.47Correct answer is between '2.4,2.47'. 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 If the initial approximation is x0=2.5 then the first approximation of (15)(1/3) using Newton Raphson method is …………….. [Write the answer upto two decimal points]a)2.4b)2.47Correct answer is between '2.4,2.47'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the initial approximation is x0=2.5 then the first approximation of (15)(1/3) using Newton Raphson method is …………….. [Write the answer upto two decimal points]a)2.4b)2.47Correct answer is between '2.4,2.47'. Can you explain this answer?.
Solutions for If the initial approximation is x0=2.5 then the first approximation of (15)(1/3) using Newton Raphson method is …………….. [Write the answer upto two decimal points]a)2.4b)2.47Correct answer is between '2.4,2.47'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of If the initial approximation is x0=2.5 then the first approximation of (15)(1/3) using Newton Raphson method is …………….. [Write the answer upto two decimal points]a)2.4b)2.47Correct answer is between '2.4,2.47'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If the initial approximation is x0=2.5 then the first approximation of (15)(1/3) using Newton Raphson method is …………….. [Write the answer upto two decimal points]a)2.4b)2.47Correct answer is between '2.4,2.47'. Can you explain this answer?, a detailed solution for If the initial approximation is x0=2.5 then the first approximation of (15)(1/3) using Newton Raphson method is …………….. [Write the answer upto two decimal points]a)2.4b)2.47Correct answer is between '2.4,2.47'. Can you explain this answer? has been provided alongside types of If the initial approximation is x0=2.5 then the first approximation of (15)(1/3) using Newton Raphson method is …………….. [Write the answer upto two decimal points]a)2.4b)2.47Correct answer is between '2.4,2.47'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If the initial approximation is x0=2.5 then the first approximation of (15)(1/3) using Newton Raphson method is …………….. [Write the answer upto two decimal points]a)2.4b)2.47Correct answer is between '2.4,2.47'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup