Numerical Methods
4th Edition
ISBN: 9780495114765
Author: J. Douglas Faires, BURDEN
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Videos
Question
Chapter 3.2, Problem 1E
a.
To determine
Using given function construct the Lagrange interpolation polynomials of degree 1 and 2 and calculate the actual error.
b.
To determine
Using given function construct the Lagrange interpolation polynomials of degree 1 and 2 and calculate the actual error.
c.
To determine
Using given function construct the Lagrange interpolation polynomials of degree 1 and 2 and calculate the actual error.
d.
To determine
Using given function construct the Lagrange interpolation polynomials of degree 1 and 2 and calculate the actual error.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
For on f (x) = ln (x + 1) and let x_0 = 0: x_1 = 0.6; x_2 = 0.9 construct the Lagrange polynomial of degree one and the Lagrange polynomial of degree two to approximate the value of f (0.45) use that of one to find the absolute error
For which value of x does the Maclaurin polynomial Tn satisfy Tn(x) = f (x), no matter what f is?
Find the fourth-degree Taylor polynomial T4(x) for the function f(x)=cosx at the number x=π/3.
T4(x)=
Chapter 3 Solutions
Numerical Methods
Ch. 3.2 - Prob. 1ECh. 3.2 - Prob. 2ECh. 3.2 - Use appropriate Lagrange interpolating polynomials...Ch. 3.2 - Use Nevilles method to obtain the approximations...Ch. 3.2 - Prob. 5ECh. 3.2 - Prob. 6ECh. 3.2 - Prob. 7ECh. 3.2 - Use the Lagrange interpolating polynomial of...Ch. 3.2 - Prob. 9ECh. 3.2 - Prob. 10E
Ch. 3.2 - Prob. 11ECh. 3.2 - Nevilles method is used to approximate f(0.5),...Ch. 3.2 - Prob. 13ECh. 3.2 - Suppose xj=j for j=0,1,2,3 and it is known that...Ch. 3.2 - Nevilles method is used to approximate f(0) using...Ch. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - A fourth-degree polynomial P(x) satisfies...Ch. 3.3 - Prob. 10ECh. 3.3 - The Newton forward divided-difference formula is...Ch. 3.3 - For a function f, the Newtons interpolatory...Ch. 3.3 - Prob. 13ECh. 3.4 - Use Hermite interpolation to construct an...Ch. 3.4 - Prob. 2ECh. 3.4 - Use the following values and five-digit rounding...Ch. 3.4 - Let f(x)=3xexe2x Approximate f(1.03) by the...Ch. 3.4 - Prob. 5ECh. 3.4 - The following table lists data for the function...Ch. 3.4 - A car traveling along a straight road is clocked...Ch. 3.4 - Prob. 8ECh. 3.5 - Prob. 1ECh. 3.5 - Prob. 2ECh. 3.5 - Construct the natural cubic spline for the...Ch. 3.5 - The data in Exercise 3 were generated using the...Ch. 3.5 - Construct the clamped cubic spline using the data...Ch. 3.5 - Repeat Exercise 4 using the clamped cubic splines...Ch. 3.5 - Prob. 7ECh. 3.5 - Construct a natural cubic spline to approximate...Ch. 3.5 - Prob. 9ECh. 3.5 - Prob. 10ECh. 3.5 - Prob. 11ECh. 3.5 - A clamped cubic spline s for a function f is...Ch. 3.5 - Prob. 13ECh. 3.5 - Prob. 14ECh. 3.5 - Suppose that f(x) is a polynomial of degree 3....Ch. 3.5 - Suppose the data xi,fxi)i=1n lie on a straight...Ch. 3.5 - The data in the following table give the...Ch. 3.5 - Prob. 18ECh. 3.5 - Prob. 19ECh. 3.5 - It is suspected that the high amounts of tannin in...Ch. 3.6 - Prob. 1ECh. 3.6 - Prob. 2ECh. 3.6 - Construct and graph the cubic BĂ©zier polynomials...Ch. 3.6 - Prob. 4E
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Find the third Taylor polynomial of the function f (x) = ex, with x0= 0arrow_forwardFor the function f(x)=√(x+1),Tn, n. Find the approximations asked around x=8 for f(10), including the degree Taylor polynomial approximation. T1=? T2=? Use 4 digits after the comma for decimal numbers in your answers. However, make sure that all digits are preserved during calculations.arrow_forwardFind the 3rd degree Taylor polynomial for the function below centered at pi/3 f(x)=sin xarrow_forward
- Find the Taylor polynomial of degree 3 for sin(x), for x near 0:P3(x)= Approximate sin(x) with P3(x) to simplify the ratio:sin(x)/x= Using this, conclude the limit:lim x→0 sin(x)/x=arrow_forwardSuppose if we use a linear Lagrange polynomial, differentiate and evaluate at x = x0 what formula will we get?arrow_forwardDetermine the degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicated value of x to be less than 0.001 ...f(x) = sin x, approximate f(0.3)arrow_forward
- determine the degree of the maclaurin polynomial required for the error in the approximation of the function f(x)= cos x at x=0.75 to be less than 0.001arrow_forwardFind the third Taylor polynomial for the function f(x) = tan x, centered at c = - /4arrow_forwardWrite the Taylor polynomial T5(x), for the function f(x)=cos(x)f(x)=cos(x) centered at x=0. T5(x)= ? Can you please help me to find the fifth term of x?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Power Series; Author: Professor Dave Explains;https://www.youtube.com/watch?v=OxVBT83x8oc;License: Standard YouTube License, CC-BY
Power Series & Intervals of Convergence; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=XHoRBh4hQNU;License: Standard YouTube License, CC-BY