The sequence of values given by the iterative formula with initial value x 1 = 1, converges

Question:

The sequence of values given by the iterative formulawith initial value x₁ = 1, converges to α.

a. Use this formula to find α correct to 2 decimal places, showing the result of each iteration to 4 decimal places.

b. Show that α also satisfies the equation tan x − 2x = 0 where 1 ≤ x < π/2.

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

Step by Step Answer:

Related Book For book-img-for-question

Cambridge International AS & A Level Mathematics Pure Mathematics 2 & 3 Coursebook

ISBN: 9781108407199

1st Edition

Authors: Sue Pemberton, Julianne Hughes, Julian Gilbey

See More Books

Question Posted: Apr 05, 2023 11:08 AM

See More Questions

The equation has one real root, denoted by . a. Find, by calculation, the pair of consecutive integers between which lies. b. Show that, if a sequence of values given by the iterative formula...
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...
KYC's stock price can go up by 15 percent every year, or down by 10 percent. Both outcomes are equally likely. The risk free rate is 5 percent, and the current stock price of KYC is 100. (a) Price a...
The quality of information that gives assurance that it is reasonably free of error and bias and is a faithful representation is: a Neutrality b Reliability c Relevance d Verifiability
1. How does BNI reinforce the importance of selling based on benefits? 2. List three things that BNI does that you could adopt to help build business relationships.
What weakness is inherent in the accounting rate of return when it is used as an investment criterion? LO.1
91.17
Prepare the monthly income statement, monthly statement of owners equity, and the balance sheet at August 31, 2014, for Krishna Cleaning Company from the data provided in the adjusted trial balance...
Question 1 10 The Jumping Jungle has 40,000 shares of $50 par, 2% cumulative preferred stock and 100,000 shares of $25 par common stock. The following amounts were distributed as dividends:...
a. On the same axes, sketch the graphs of y = ln(x + 1) and y = 3x 4. b. Hence deduce the number of roots of the equation ln(x + 1) 3x + 4 = 0.
The equation of a curve is x 2 y + y 2 = 6x. i. Show that ii. Find the equation of the tangent to the curve at the point with coordinates (1, 2), giving your answer in the form ax + by + c = 0. dy dx...
Refer to the transactions in E6-8. In E8 July 5 Purchases 20 laptop computers on account from Red River Supplies for $1,500 each, terms 3/10, n/30. July 8 Returns to Red River two laptops that had...
The curved rod has a diameter $d$. Determine the vertical displacement of end $B$ of the rod. The rod is made of material having a modulus of elasticity of $E$. Consider only bending strain...
If the inertial measurement system were written in C++ according to the design fragment described in Chapter 5, describe the testing strategy you would use. If possible, try to design some test cases.
Determine the displacement at point $C$ of the W14 $\times 26$ beam made from A992 steel. 8 kip A -5 ft 5 ft. B C -5 ft 5 ft- 8 kip D
The beam is subjected to the loading shown. Determine the slope at $B$ and displacement at $C$. $E I$ is constant. Ta Mo C b B
A mass, connected to a damper as shown in Fig. 14.30, is subjected to a force $F(t)$. Find the frequency-response function $H(\omega)$ for the velocity of the mass. m F(t) y(1) FIGURE 14.30...
Cole Allen, the bookkeeper for Brentwood Company, asks for your help in identifying whether the following transactions should be reported on the corporations statement of cash flows. Prepare a list...
Synthesize the products by drawing out reagents and intermediates along the way. `N H. OH HO HO
Calculate the range, average deviation, and standard deviation for the following five distributions: a. 1, 2, 3, 4, 5, 6, 7, 8, 9 b. 24, 23, 22, 21, 0, 1, 2, 3, 4 c. 10, 20, 30, 40, 50, 60, 70, 80,...
The results of a recent survey indicate that the average new car costs $23,000 with a standard deviation of $3,500. The price of cars is normally distributed. a. If someone bought a car for $32,000,...
A survey of college students was conducted during final exam week to assess the number of cups of coffee consumed each day. The mean number of cups was 5 with a standard deviation of 1.5 cups. The...
Pottery Ranch Inc. has been manufacturing its own finials for its curtain rods. The company is currently operating at 100% of capacity, and variable manufacturing overhead is charged to production at...
3. How much life insurance do you need? Calculating resources - Part 2 Aa Aa E Paolo and Maria Rossi have completed Step 1 of their needs analysis worksheet and determined that they need $2,323,000...
On March 1, LGE asks to extend its past-due $1,200 account payable to Tyson, Tyson agrees to accept $200 cash and a 180-day, 8%, $1,000 note payable to replace the account payable. (Use 360 days a...

The sequence of values given by the iterative formula with initial value x 1 = 1, converges

Question:

Xn+1 = x₁(1+ sec² xn) - tan Xn sec² x₁ - 1

Step by Step Answer:

ANSWER a To find we can start with x1 1 and iteratively apply the formula until the values ...View the full answer

Cambridge International AS & A Level Mathematics Pure Mathematics 2 & 3 Coursebook

Students also viewed these Mathematics questions