Why is a Non-Zero Root Used in Newton's Method for Sin(x) = x^2?

In summary, Newton's Method is a mathematical problem-solving technique that uses iterative steps to find the roots or solutions to a given function. It starts with an initial guess and uses the derivative of the function to improve the estimate until a desired level of accuracy is achieved. It is commonly used in various fields and has advantages such as speed and efficiency, but also limitations such as convergence issues and the need for a continuous second derivative.
  • #1
Miike012
1,009
0
Question:
Use Newtons method to approximate the indicated root of the equation correct to six decimal places.

The positive root of sin(x) = x^2

The answer is ...0.876726

Why did they pick this when the obvious root is 0?

Sin(0) = (0)^2 = 0
 
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  • #2
There are two roots - they want you to find the other one.
The one that it actually helps to use Newton's method for.
 
  • #3
Yes, they wouldn't ask you to use Newton's Method if they only wanted the trivial root. Try to start with a first approximation that is near the root. I'd try 1.
 

Related to Why is a Non-Zero Root Used in Newton's Method for Sin(x) = x^2?

1. What is Newton's Method Problem?

Newton's Method Problem is a mathematical problem that involves finding the roots or solutions to a given function. It is a numerical method that uses iterative steps to approximate the root of a function.

2. How does Newton's Method work?

Newton's Method works by starting with an initial guess or estimate for the root of a function. It then uses the derivative of the function at that point to calculate a better estimate for the root. This process is repeated until the desired level of accuracy is achieved.

3. What is the purpose of Newton's Method?

The purpose of Newton's Method is to find the roots or solutions to a given function. It is commonly used in mathematics, physics, and engineering to solve a wide range of problems, such as finding the maximum or minimum of a function.

4. What are the advantages of using Newton's Method?

One of the main advantages of Newton's Method is its speed and efficiency. It can converge to the root of a function much faster than other methods, making it a popular choice for solving complex problems. It is also relatively easy to implement and can handle a wide range of functions.

5. What are the limitations of Newton's Method?

Newton's Method may not always converge to the root of a function, especially if the initial guess is not close enough to the root. It also requires the function to have a continuous second derivative, which may not always be the case. Additionally, it can be computationally expensive for complex functions.

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