Find maximal interval for which the newton method iterates

Assignment Help Mathematics

Reference no: EM131009076

1) Consider applying Newton's method to find the root α = 0 of the equation sin (x) = 0. Find the maximal interval (-r, r) for which the Newton method iterates will converge to α for any choice of x₀ in (-r, r).

Hint: Draw a graph of y = sin (x) and graphically interpret the placement of x₀ and x₁.

2) Use Newton's method to solve the equation:

0.25x2 - xsin (x) - 0.5 cos (2x) + .5 = 0 with P₀ = π/2.

Iterate using Newton's method until the accuracy of 10^-5 is obtained. Explain why the result seems unusual for the Newton's method. Also, solve the equation with P₀ = 5π and P₀ = 10π.

Reference no: EM131009076

Questions Cloud

Discuss future implications of this act success or failure : Discuss the potential success or failure of this act. Justify your opinion. Discuss future implications of this act's success or failure

Why the light vibrating in the plane of incidence : Why the light vibrating in the plane of incidence is not reflected at Brewster''s angle

How you could enhance the organisations image : How you could model high standards of management behaviour ad performance - How you could enhance the organisations image

Identify the project scope the pricing cost control : Generate a paper that explains how you are planning to incorporate quality management initiatives into the project environment. Identify the project scope, the pricing, cost control and estimating techniques to be employed, as well as a summary of..

Find maximal interval for which the newton method iterates : Consider applying Newton's method to find the root α = 0 of the equation sin (x) = 0. Find the maximal interval (-r, r) for which the Newton method iterates will converge to α for any choice of x0 in (-r, r).

Identify the independent variable and dependent variable : Explain whether the researcher should use an independent-samples t-test or a related-samples t-test for this scenario. Provide a rationale for your decision. Identify the independent variable and dependent variable

Create a chart evaluating three age-related stereotypes : Create a chart evaluating three age-related stereotypes listing evidence that supports the stereotype (if it exists) and evidence that contradicts the stereotype

Problem regarding the delivery service : A company must decide which of two delivery services they will contract with. During a recent trial period, they shipped numerous packages with each service and have kept track of how often deliveries did not arrive on time. Here are the data.

Estimate the total amount of the drug present : A patient receives 3 milligrams of a certain drug each day. Each day the body eliminates 20% of the amount of drug present in the system. Estimate the total amount of the drug present after extended treatment, immediately after a dose is given.

User Account

All Pages