Preparation open tasks for the exam in Mathematical Analysis. BISECTION METHOD 1. Using the bisection method...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Preparation open tasks for the exam in Mathematical Analysis. BISECTION METHOD 1. Using the bisection method within three steps and initial interval [3, 4], find a decimal approximation of 100 and estimate the error of the approximation. Sample solution: We use the interval [3, 4] as our initial interval. Since we are considering the fourth root, to determine whether the approximation is an overestimate or an underestimate, we will examine the fourth power of the approximation. Step 1 Interval Midpoint Power of 4 [3, 4] 3.5 (3.5) 10 [3, 3.5] 3.25 (3.25) > 10 [3, 3.25] 3.125 (2.125) <10 2 3 The value is in the interval (3.125, 3.25). If we assume that 100 3.1875 (midpoint), then the error of this approximation will not exceed 0.03125 (half of the length of the interval). 2. Using the bisection method within three steps and initial interval [1, 3], find a decimal approximation of 35 and estimate the error of the approximation. 3. Using the bisection method within three steps and initial interval [2, 3], find a decimal approximation of 40 and estimate the error of the approximation. 4. Using the bisection method within three steps and initial interval [4, 6], find a decimal approximation of 31 and estimate the error of the approximation. STUDY OF A SINGLE-VARIABLE FUNCTION Find (by investigating sign of derivatives) where each of the following functions are increasing and where they are decreasing. Then find the extrema, and say whether each extremum is a maximum or a minimum. 1. f(x) = x-3x+6 Answer: increasing on (-0, 0] and [2, c), decreasing on [0,2]. f(2) = 2,(0) = 6. 2. f(x)=x+ Answer: increasing on (-00, -1)] and [1, 0), decreasing on [-1, 0) and (0, 1). fin(1) = 2, max(-1)=-2. 3. f(x) = x+ Answer: increasing on (-0, 0] and c), decreasing on [0, () = + 2. 4. f(x) = x+ Answer: increasing on (-, 0] and [2, ), decreasing on (0, 2). min(2) = + 2. INTEGRAL SUMS 1. Given a function f: [-1,0] [0, 1], f(x) = x sketch (accurately!) the graph of this function. Divide the interval [1,0] into 4 equal parts and, choosing the right bound of each interval to calculate the heights Preparation open tasks for the exam in Mathematical Analysis. BISECTION METHOD 1. Using the bisection method within three steps and initial interval [3, 4], find a decimal approximation of 100 and estimate the error of the approximation. Sample solution: We use the interval [3, 4] as our initial interval. Since we are considering the fourth root, to determine whether the approximation is an overestimate or an underestimate, we will examine the fourth power of the approximation. Step 1 Interval Midpoint Power of 4 [3, 4] 3.5 (3.5) 10 [3, 3.5] 3.25 (3.25) > 10 [3, 3.25] 3.125 (2.125) <10 2 3 The value is in the interval (3.125, 3.25). If we assume that 100 3.1875 (midpoint), then the error of this approximation will not exceed 0.03125 (half of the length of the interval). 2. Using the bisection method within three steps and initial interval [1, 3], find a decimal approximation of 35 and estimate the error of the approximation. 3. Using the bisection method within three steps and initial interval [2, 3], find a decimal approximation of 40 and estimate the error of the approximation. 4. Using the bisection method within three steps and initial interval [4, 6], find a decimal approximation of 31 and estimate the error of the approximation. STUDY OF A SINGLE-VARIABLE FUNCTION Find (by investigating sign of derivatives) where each of the following functions are increasing and where they are decreasing. Then find the extrema, and say whether each extremum is a maximum or a minimum. 1. f(x) = x-3x+6 Answer: increasing on (-0, 0] and [2, c), decreasing on [0,2]. f(2) = 2,(0) = 6. 2. f(x)=x+ Answer: increasing on (-00, -1)] and [1, 0), decreasing on [-1, 0) and (0, 1). fin(1) = 2, max(-1)=-2. 3. f(x) = x+ Answer: increasing on (-0, 0] and c), decreasing on [0, () = + 2. 4. f(x) = x+ Answer: increasing on (-, 0] and [2, ), decreasing on (0, 2). min(2) = + 2. INTEGRAL SUMS 1. Given a function f: [-1,0] [0, 1], f(x) = x sketch (accurately!) the graph of this function. Divide the interval [1,0] into 4 equal parts and, choosing the right bound of each interval to calculate the heights
Expert Answer:
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
Students also viewed these mathematics questions
-
This assignment asks that you reflect on the multiple ways you may identify yourself. In the context of human diversity, there are many ways in which you are different from, and the same as, other...
-
CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...
-
Two moles of an ideal monatomic gas go through the cycle abc. For the complete cycle, 800 J of heat flows out of the gas. Process ab is at constant pressure, and process bc is at constant volume....
-
Georgia Orchards produced a good crop of peaches this year. After preparing the following income statement, the company believes it should have given its No. 3 peaches to charity and saved its...
-
What is meant by the term path?
-
Assume the following exceptions to prescribed control procedures over sales transactions occurred in the Lane Company: 1. A shipment to a bona fide customer was not billed. 2. A sales invoice was...
-
If the Albany highway system described in Problem 29 has revised flow capacities as shown in the following network, what is the maximal flow in vehicles per hour through the system? How many vehicles...
-
Problem assignmemnt The newly appointed accountant of a start-up company Pioneer Limited, which has received funding from two sharks jointly in the Shark Tank against the issue of debentures, has...
-
In this step you are required to forecaste for the next five (5) years the key accounting drivers of sales growth, profit margin, asset turnover and Return on net operating assets and including these...
-
What is the main business theme (EBT) for fairness?
-
Is the word fairness the most appropriate candidate for creating a stable pattern? If so, give reasons.
-
Could fairness pattern be applied to all domains?
-
What kinds of qualifications might a statute place on someone who is in a dating relationship? What problems might these qualifications pose?
-
Compare this stable pattern with the ones that are designed by using a traditional method.
-
You want to predict the average price of gasoline (regular, unleaded) in Minnesota in the coming year. Propose a regression with no less than 3 and no greater than 5 exogeneous variables to make this...
-
This problem continues the Draper Consulting, Inc., situation from Problem 12-45 of Chapter 12. In October, Draper has the following transactions related to its common shares: Oct 1 Draper...
-
Olive Corporation was formed and began operations on January 1, 2012. The corporation's income statement for the year and the balance sheet at year-end are presented below. The corporation made...
-
Professor Patricia (Patty) Pate is retired from the PalmSprings Culinary Arts Academy (PSCAA). She is a single taxpayer and is 68 years old. Patty lives at 98 Colander Street, Henderson, NV 89052....
-
The following additional information is available for the Dr. Ivan and Irene Incisor family. The Incisors own a rental beach house in Hawaii. The beach house was rented for the full year during 2012...
-
True or False. A multi-degree-of-freedom system can have six of the natural frequencies equal to zero.
-
True or False. The modal analysis of a \(n\)-degree-of-freedom system can be conducted using \(r\) modes with \(r
-
True or False. The modal damping ratio denotes damping in a particular normal mode.
Study smarter with the SolutionInn App