Show the cubic equation x 3 2x 1 = 0 has a root near x

Question:

Show the cubic equation x³ – 2x – 1 = 0 has a root near x = 2. Prove that the iteration

fails to converge to that root. Devise a simple iteration formula for the root of the equation, and use it to find the root to 6dp.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Modern Engineering Mathematics

ISBN: 9781292253497

6th Edition

Authors: Glyn James

See More Books

Question Posted: Jan 16, 2024 03:02 AM

See More Questions

Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...
In a standard non-compete agreement, what are the interests and positions of the parties involved? What is the relative power and leverage of the parties as they enter into a typical non-compete...
a. Show that the equation ln(x + 1) + 2x 4 = 0 has a root between x = 1 and x = 2. b. Use the iterative formula with an initial value of = 1.5 x 1 to find the value of correct places. Xn+l 4 - In(x...
Consider the following propositions: p: 2 is the smallest prime q: 6 is a perfect square Represent the proposition "2 is the smallest prime but 6 is not a perfect square" using logical connectives....
You are writing energy balances for a compound for which you cannot find heat capacity or latent heat data. All you know about the material are its molecular formula (C7H12N) and that it is a liquid...
P Company holds an 80% interest in SFr Company, a Swiss company. A trial balance for P Company and SFr Company at December 31, 2009, and other data are given in Problems 13-9 and 13-10. The following...
Airline pricing, considerations other than cost in pricing. Air North is about to introduce a daily round-trip flight from Toronto to Vancouver. Air North offers only one class of seatsComfort Class,...
1. How sensitive is the NPV to changes in the price of the new smart phone? 2. How sensitive is the NPV to changes in the quantity sold of the new smart phone? Shelley Couts, the owner of Conch...
Home Lawn and Garden Company, Inc. had these transactions during the current period. March 22 Issued 25,000 shares of $4 stated value common stock for cash of $160,000. May 11 Issued 8,000 shares of...
The equation f(x) = 0 has a root at x = . Show that rewriting the equation as x = x + f(x), where is a constant, yields a convergent iteration for a if = 1/f(x 0 ) and x 0 is sufficiently close to...
If = f() but the iteration x n+1 = f (x n ) fails to converge to the root a, under what condition on f(x) will the iteration x n+1 = f 1 (x n ) converge?
Think about what it means to be a part of a teama successful team. What makes one team more successful than another? What does each team member need to do in order for their team to be successful?...
From the following electrochemical cells write: (a) the electrode half reactions for oxidation and reduction (b) the overall cell reaction (c) the NERNST equation for the emf for each of the cells...
Use the range rule of thumb to identify the values that are significantly low, the values that are signficantly high, and the values that are neither significantly low nor significantly high. A test...
On January 1, Year 1, Handy Company (Handy) purchased 70% of the outstanding common shares of Dandy Limited (Dandy) for $11,900. On that date, Dandys shareholders equity consisted of common shares of...
CarFind Inc. showed the following equity information at December 31, 2019. Common shares, unlimited shares authorized; 4,900,000 shares issued and outstanding Retained earnings $1,045,000 1,385,000...
Cell Phone Radiation Listed below are the measured radiation rates (in W/kg) corresponding to these cell phones: iPhone X, iPhone 7, Google Pixel, Samsung Galaxy 58, OnePlus 5, Motorola VE465, LG G3,...
Joe, Thea, and Taylor invested in a partnership in the ratio 1:4:7, respectively. Years later, when the partnership was worth $1.6 mil- lion, Thea decides to go to graduate school and sells her part...
Highland Theatre is owned by Finnean Ferguson. At June 30, 2014, the ledger showed the following: Cash, $6,000; Land, $100,000; Buildings, $80,000; Equipment, $25,000; Accounts Payable, $5,000;...
The box beam is constructed from four boards that are fastened together using nails spaced along the beam every 2 in. If a force P = 2 kip is applied to the beam, determine the shear force resisted...
The member consists of two plastic channel strips 0.5 in. thick, glued together at A and B. If the distributed load has a maximum intensity of w0 = 3 kip>ft, determine the maximum shear stress...
The member consists of two plastic channel strips 0.5 in. thick, glued together at A and B. If the glue can support an allowable shear stress of Ï allow = 600 psi, determine the maximum...
The payroll register of Ruggerio Co. indicates $13,800 of social security withheld and $3,450 of Medicare tax withheld on total salaries of $230,000 for the period. Federal withholding for the period...
All of the following are included on Form 1040, page 1, EXCEPT: The determination of filing status. The Presidential Election Campaign check box. The income section. The paid preparer signature line.
Question One: (25 marks) (X) Inc. purchased 80% of the outstanding voting shares of (Y) for $360,000 on July 1, 2017. On that date, (Y) had common shares and retained earnings worth $180,000 and...

Show the cubic equation x 3 2x 1 = 0 has a root near x

Question:

Xn+1 =(x-1)

Step by Step Answer:

Setting fx x 2x 115 0 and 2 0 sofhas a zero between 15 and 2 3 d dx 22x1 2 x SO Xn...View the full answer

Modern Engineering Mathematics

Students also viewed these Sciences questions