f(x) = x 2 6x + 1 a. Show that the equation f(x) = 0 can

Question:

f(x) = x² − 6x + 1

a. Show that the equation f(x) = 0 can be written as x = √6x + 1.

b. Sketch on the same axes the graphs of y = x and y = √6x - 1.

c. Write down the number of roots of f(x).

d. d Use your diagram to explain why the iterative formula converges to a root of f(x) when x₀ = 2. f(x) = 0 can also be rearranged to form the iterative formula

e. By sketching a diagram, explain why the iteration diverges when x₀ = 10.

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

Step by Step Answer:

Related Book For book-img-for-question

Pearson Edexcel A Level Mathematics Pure Mathematics Year 2

ISBN: 9781292183404

1st Edition

Authors: Greg Attwood, Jack Barraclough, Ian Bettison, David Goldberg, Alistair Macpherson, Joe Petran

See More Books

Question Posted: Aug 17, 2023 03:09 AM

The fatigue data for a brass alloy are given as follows: (a) Make an S?N plot (stress amplitude versus logarithm cycles to failure) using these data. (b) Determine the fatigue strength at 5 ? 10 5...
In Exercises, match the correct graph AF to the function without using your calculator. Then, if you have a graphing calculator, use it to check your answers. Each graph in this group shows x and y...
In Exercises, match the correct graph AF to the function without using your calculator. Then, if you have a graphing calculator, use it to check your answers. Each graph in this group shows x and y...
Explain how to transform sin tan + cos into sec.
Olympic sports has a markup of $280 on a Schwinn Bowflex. If this is a 35% markup on selling price, find a) The selling price b) The cost c) The cost as a percent of selling price
If a country is at a point on its PPF where the slope of the PPF is flatter than the slope of the CIC touching that same point, then the standard of living would rise if outputs of the two goods...
What is the aim of PRINCE2? AppendixLO1
Analysis of Stockholders Equity The Stockholders Equity section of the December 31, 2010, balance sheet of Eldon Company appeared as follows: Preferred stock, $30 par value, 5,000 shares authorized,...
business law question All contract rights assignable. are True False
a. On the same axes, sketch the curves of y = p(x) and y = q(x). p(x) = 4 x 2 and q(x) = e x . b. State the number of positive roots and the number of negative roots of the equation x 2 + e x 4 =...
a. Calculate f(3.9) and f(4.1). b. Explain why the equation f(x) = 0 does not have a root in the interval 3.9 < x < 4.1. The equation f(x) = 0 has a single root, . c. Use algebra to find the exact...
Assume that the distribution of x is f (x) = 1/, 0 x . In random sampling from this distribution, prove that the sample maximum is a consistent estimator of . Note: You can prove that the maximum...
Melannie Inc. sold $8,200 worth of merchandise on June 1, 2015 on credit. After inspecting the inventory, the customer determined that 10% of the items were defective and returned them to Melannie...
2. (20 marks) A firm wishes to produce a single product at one or more locations so that the total monthly cost is minimized subject to demand being satisfied. At each location there is a fixed...
Evaluate your own negotiation way. Do you have one? how you consider having an excellent negotiaiton skill could help any business person to achieve its goals.
j. Interest was accrued on the note receivable received on October 17 ($100,000, 90-day, 9% note). Assume 360 days per year. Date Description Dec. 31 Interest Receivable Interest Revenue Debit Credit
A Chief Risk Officer (CRO) is interested in understanding how employees can benefit from AI assistants in a way that reduces risk. How do you respond
A helium-filled balloon escapes a child's hand at sea level and 20.0C. When it reaches an altitude of 3600 m, where the temperature is 5.0C and the pressure only 0.68 atm, how will its volume compare...
Using Apple, demonstrate how the differentiation strategy can be well implemented.
Refer to Exercise 4.74. Draw histograms of the data. What have you learned?
In Exercise 4.71 you calculated quartiles. Draw histograms instead and compare the results.
a. Calculate the coefficients of the least squares line for the data in Example 3.7. b. Interpret the coefficients. c. Is this information more useful than the information extracted from the scatter...
Create a Data Table to depict the future value when you vary the interest rate and the investment amount. Use the following assumptions: Interest Rates: Investment Amounts:-10.0% $10,000.00 -8.0%...
Isaac earns a base salary of $1250 per month and a graduated commission of 0.4% on the first $100,000 of sales, and 0.5% on sales over $100,000. Last month, Isaac's gross salary was $2025. What were...
Calculate the price, including both GST and PST, that an individual will pay for a car sold for $26,995.00 in Manitoba. (Assume GST = 5% and PST = 8%) a$29,154.60 b$30,234.40 c$30,504.35 d$28,334.75...

f(x) = x 2 6x + 1 a. Show that the equation f(x) = 0 can

Question:

n I-"x9 = 1+"x

Step by Step Answer:

a x 6x 1 0 x 6x 1 x 6x 1 ...View the full answer

Pearson Edexcel A Level Mathematics Pure Mathematics Year 2

Students also viewed these Mathematics questions