Use the error formulas in Theorem 8.6 to estimate the errors in approximating the integral, with n
Question:
Use the error formulas in Theorem 8.6 to estimate the errors in approximating the integral, with n = 4, using
(a) The Trapezoidal Rule and
(b) Simpson’s Rule.
Transcribed Image Text:
THEOREM 8.6 Errors in the Trapezoidal Rule and Simpson's Rule If f has a continuous second derivative on [a, b], then the error E in approximating f f(x) dx by the Trapezoidal Rule is |E| ≤ (b − a)³ 12n² |E| ≤ -[max [f"(x)], a ≤x≤ b. Trapezoidal Rule Moreover, if f has a continuous fourth derivative on [a, b], then the error E in approximating fa f(x) dx by Simpson's Rule is (b − a)³ 180n4 -[max f(x)], a ≤ x ≤ b. Simpson's Rule
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 75% (4 reviews)
answer We have the definite integral 0 1 ex3 dx that we want to approximate using the Trapezoidal Ru...View the full answer
Answered By
Nikka Ella Clavecillas Udaundo
I have a degree in psychology from Moi University, and I have experience working as a tutor for students in both psychology and other subjects. I am passionate about helping students learn and reach their potential, and I firmly believe that everyone has the ability to succeed if they receive the right support and guidance. I am patient and adaptable, and I will work with each individual student to tailor my teaching methods to their needs and learning style. I am confident in my ability to help students improve their grades and reach their academic goals, and I am excited to work with a new group of students.
0.00
0 Reviews
10+ Question Solved
Related Book For
Calculus Of A Single Variable
ISBN: 9781337275361
11th Edition
Authors: Ron Larson, Bruce H. Edwards
Question Posted:
Students also viewed these Mathematics questions
-
In Exercises use the error formulas in Theorem 4.20 to estimate the errors in approximating the integral, with n = 4, using (a) The Trapezoidal Rule (b) Simpson's Rule. Data from in Theorem 4.20...
-
In Exercises use the error formulas in Theorem 4.20 to estimate the errors in approximating the integral, with n = 4, using (a) The Trapezoidal Rule (b) Simpson's Rule. Data from in Theorem 4.20...
-
In Exercises use the error formulas in Theorem 4.20 to estimate the errors in approximating the integral, with n = 4, using (a) The Trapezoidal Rule (b) Simpson's Rule. Data from in Theorem 4.20...
-
Consider an asset allocation problem with one risky asset and one risk-free asset .There are four investors .Each investor maximizes a mean-variance utility function to make their optimal investment...
-
Donald Tweedt started a company to produce and distribute natural fertilizers. Donalds company sells two fertilizers that are wildly popular: green fertilizer and compost fertilizer. Green...
-
5. The burning of organic compounds involves a chemical reaction with oxygen from the air. This reaction is called a combustion reaction. Most organic compounds react with oxygen to produce carbon...
-
Flash Ltd manufactures eReaders and is considering expanding production. A distributor has asked the company to produce a special order of 6000 eReaders. The eReaders will be sold using a different...
-
Put Corporation acquired a 90 percent interest in Sam Corporation at book value on January 1, 2011. Intercompany purchases and sales and inventory data for 2011, 2012, and 2013, are as follows:...
-
The Olney Corporation provided the following information to their CPA. The accountant was asked to help them answer the questions listed below. Sales $ 274,000 Variable expenses 225,000 Contribution...
-
Redline Publishers, Inc., produces various manuals ranging from computer software instructional booklets to manuals explaining the installation and use of large pieces of industrial equipment. At the...
-
Use a table of integrals to find the indefinite integral. X - sec x dx
-
Use a table of integrals to find the indefinite integral. 13 1 + sin 04 - de
-
What does it mean to revalue a long-term asset? How do U.S. GAAP and IFRS differ regarding revaluation of long-term assets?
-
You work for a business with small offices in eight countries around the world. Meetings are usually facilitated via Skype, but other online communication and collaboration is a problem. Three months...
-
You work for a custom travel business that operates across the world. Your clients tend to come from your own country, but you have regular customers from over 40 others. Although you do not offer...
-
What are three techniques for deemphasizing negative news?
-
Should you use the direct or indirect approach for most routine messages? Why?
-
You work for an importexport business that has, until recently, only offered services to other businesses. Recently, you noticed the opportunity to make full use of shipping containers by offering...
-
If the pdf for Y is Find and graph FY (y). yl>
-
Separate variables and use partial fractions to solve the initial value problems in Problems 18. Use either the exact solution or a computer-generated slope field to sketch the graphs of several...
-
In Exercises use the power series to determine a power series, centered at 0, for the function. Identify the interval of convergence. 1 1 + x = = (-1)".x" n=0
-
In Exercises use the power series to determine a power series, centered at 0, for the function. Identify the interval of convergence. 1 1 + x = = (-1)".x" n=0
-
In Exercises find the Maclaurin series for the function. Use the table of power series for elementary functions. f(x) = ln(1 + x)
-
Reflect on examples of conflict in your personal, academic, or professional life. In the worksheet below, please describe an example of a recent conflict you personally experienced. Describe your...
-
What type of communication is most effective to use with 3 to 5-year-old children (early childhood)? Nonverbal communication Written communication Indirect communication Direct communication
-
Using the table below, identify an appropriate method for communicating with a supervisor for each situation listed: Situation Best method for communicating with your supervisor You are having...
Study smarter with the SolutionInn App