Please help me. Q1.2 Convergence rate and order of a sequenceAssume an iterative method generates a sequence of iterates xk that converges in such away that the errorek = |x* xk| = k/2k, for all k = 1, 2, ....Find the convergence order and convergence rate of the method in this case.Convergence order =Enter your answer hereConvergence rate =Enter your answer hereJustification:Enter your answer here

The given sequence is: ek=|x∗−xk|=k2k, for all k=1,2,3,… Find the convergence order and convergence…

Answered: Q1.2 Convergence rate and order of a…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.3: Geometric Sequences

Problem 82E

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Areas of Curved Regions the Monte Carlo method can be used to estimate the area under the graph of a function. The figure below shows the region under the graph of f(x)=x2 above the x-axis, between x=0 and x=1. if we choose a point in the square at random, probability that it lies under the graph of f(x)=x2 is the area under the graph divided by the area of the square. So if randomly select a large of points in the square, we have Modify the program from Problem 5 to carry out this Monte Carlo simulation and mate the required area.
Series Discount This is a continuation of Exercise 11. Sometimes manufacturers give more than one discount instead of a single trade discount for example, in trading with large-volume retailers. Such a series discount is quoted as a sequence of discounts, taken one after another. Suppose a manufacturer normally gives a trade discount of 45%, but it has too much of the item in inventory and so wants to sell more. In this case the manufacturer may give all retailers another discount of 15% and may perhaps extend yet another discount of 10% to a specific retailer it wants to land as a client. In this example, the series discount would be 45%, 15%, 10%, calculated one after another, like this: For an item with a suggested retail price of 100.00, applying the first discount gives 100.00-45%100.00=55.00 dollars. The second discount of 15% is applied to the 55.00 as follows: 55.00-15%55.00=46.75 dollars. Now, the third discount gives the final cost price of 46.75-10%46.75=42.08 dollars. a. Suppose an item has a suggested retail price of 80.00 and the manufacturer is giving a series discount of 25% and 10%. What is the resulting cost price? b. Suppose an item has suggested retail price of 100.00 and the manufacturer is giving a series discount of 35%, 10%, 5%. What is the resulting cost price? c. What single trade discount would give the same cost price as a series of 35%, 10%, 5%? Note: The answer is not 50% d. Explain why we could have calculated the same answer as in part b by multiplying 100.000.650.900.95. In this case, what would the 0.65, 0.90, and 0.95 represent? Trade Discount Often retailers sell merchandise at a suggested retail price determined by the manufacturer. The trade discount is the percentage discount given to the retailer by the manufacturer. The resulting price is the retailers net cost and so is called the cost price. For example, if the suggested retail price is 100.00 and the trade discount is 45%, then the cost price is 100.00-45%100=55.00 dollars. a. If an item has a suggested retail price of 9.99 and the trade discount is 40%, what is the retailers cost price? b. If item has a cost price of 37.00 and a suggested retail price of 65.00, what trade discount was used?
(a) State a necessary and sufficient condition for the convergence of the Jacobi andGauss-Seidel (GS) methods.(b) Use the previous part condition to show whether the GS method converges ordiverges to the solution of the systemx + 2y = 3,3x + (0.77)y = 4.(c) Determine x(1) by applying one iteration of the GS method with x(0) = 0.
6). Find the radius of convergence of the series. ∞ k = 1 2 · 4 · 6 2k (2k)! xk R = please show step by step clearly
Urgent numerical method Find the value around x ~ 1, which provides the equality of x ^ 3 + x - 1 = 0, by using the Newton-Raphson technique after checking the convergence criterion with a precision of 4 decimal places.
(a) Find a real root of the equation e^xtanx=1 by using iteration method and also apply Aitken's del^2 -process to accelerate the convergence. (b) FInd the value of the e^-1 when e=2.718 by using newton raphason method.
An individual is given a dose of Q units of a certain drug. the amount that remains in the bloodstream at the end of t minutes and Qe−ct, with c > 0. Suppose that the same dose is administered at successive intervals of T minutes. (a) Using series, express the amount A(k) of the drug in the bloodstream immediately after the K-th dose.(b) Find an upper bound for the amount of drug in the bloodstream after an arbitrary number of doses.(c) Find the shortest time between doses that ensures that A(k) does not exceed a certain level M, M > Q.
Suppose that Newton’s method is applied to find the solution p = 0 ofthe equation e^x − 1 − x −1/2x^2 = 0. It is known that, starting with any p0 > 0, the sequence {pn} produced by the Newton’s method is monotonically decreasing (i.e., p0 > p1 > p2 > · · ·) and converges to 0.Prove that {pn} converges to 0 linearly with rate 2/3. (hint: use L’Hospital rule repeatedly. )
i. For a convergent real sequence sn and a real number a, show that if sn ≥ a for all but finitely many values of n, then limn→∞ sn ≥ a.ii. For each value of a ∈ ℝ, give an example of a convergent sequence sn with sn > a for all n, but where limn→∞ sn = a.
∑∞ ((−1)^n−1(1−n)) /(3n−n^2) n=1 Find if the series converges or diverges! Find the limit if it converges.

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