When do you use newton's method?
Charles ArochaIf you have a real valued function and can determine its derivative at any point, the Newton method is a means of developing increasingly better approximations to a root of the function.
It would not be used if the function and its derivative allowed for simple decomposition to solve for exact roots.
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Axel AlvarezNewton's method is used to find successively better approximations to the roots (or zeroes) of a real-valued function. It's particularly useful when the function is differentiable and its derivative is easy to compute. This method is commonly employed in numerical analysis and optimization problems where an analytical solution is difficult or impossible to find. Additionally, Newton's method converges quickly to the root if the initial guess is sufficiently close to the actual root.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- Use Newton's method with the specified initial approximation x1 to find x3, the third approximation to the root of the given equation. (Round your answer to four decimal places.) What is x3?
- At what approximate rate (in cubic meters per minute) is the volume of a sphere changing at the instant when the surface area is 4 square meters and the radius is increasing at the rate of 1/6 meters per minute?
- If the rate at which water vapor condenses onto a spherical raindrop is proportional to the surface area of the raindrop, show that the radius of the raindrop will increase at a constant rate?
- A beacon on a lighthouse is one mile from shore, and revolves at 10PI Radians per minute. What is the speed with which the light sweeps across the straight shore as it lights the sand 2 miles from the lighthouse?
- A sector of a circle whose radius is r and whose angle is theta has a fixed perimeter P. How do you find the values of r and theta so that the area of the sector is a maximum?
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