Question: (15 points). Let f(x)=ex+e-xin the interval -1,1.(a) Construct the Lagrange interpolating polynomial P2(x) for f(x) using the nodesx0=-1,x1=0,x2=1.(b) Find a bound for the absolute error

(15 points). Let f(x)=ex+e-xin the interval -1,1.(a) Construct the Lagrange interpolating polynomial P2(x) for f(x) using the nodesx0=-1,x1=0,x2=1.(b) Find a bound for the absolute error on the interval -1,1.(c) Compute the integral -11P2(x)dx and compare itto the actual value -11f(x)dx.(15 points). Let f(x)=ex+e-xin the interval -1,1.(a) Construct the Lagrange interpolating polynomial P2(x) for f(x) using the nodesx0=-1,x1=0,x2=1.(b) Find a bound for the absolute error on the interval -1,1.(c) Compute the integral -11P2(x)dx and compare itto the actual value -11f(x)dx.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

For this question let f x ln x and let ro 1 1 1 x 1 3 and x3 1 4 a Construct the Lagrange interpolating polynomials L3 k x for k 0 3 b Use your answer to construct the interpolating polynomial P3 x...

o, I'm in need of answers to these questions. You can use an excel sheet of you need or a calculator. I write fantastic reviews as well! 1.) Surgical complications: A medical researcher wants to...

please code these questions 3 and 4 on matlab urgent assistance needed with full details this is all info i have Lagrange Polynomial Interpolation Recall, given p + 1 distinct points {Xi}}=0, the...

interpolation and the Lagrange polynomial 5. Polynomial Irrte rpolation. {a} Use the Lagrange interpolation process to obtain a polynomial of least degree that assumes these values. 1 I] 2 3 4 y i"...

3. (a) (10 pts.) Use Algorithm 3.3 (or, equivalently, Table 3.16 and the discussion on page 137) to find the Hermite interpolating polynomial H(x) approximating the function f(x) = sin x cos x on...

Background: Simpson's 3/8 Method In Simpson's 3/8 Method, a cubic (third-order) polynomial is used to approximate the f(x) p(x)dx=P[x]dx Equation 1 where P(x)=x; +2(x-x)+43(x-x1)(x-x2)+a_{x-x)(x -...

Please answer each question by entering the most nearly correct answer (a, b, c, d) in the blank on the left. ____1. The approximation cos(x) 1 - x2 /2 + x4 /24 is to be used over [-1,1]. The...

____1. When approximating e x by a truncated Taylor series (expanded about x=0), how many terms would be required to keep the absolute value of the error below 10 -3 over the interval [-1,1] ? a. 3...

Find the least squares line through the points: (-3. 3). (-1. 2). (0-1). (1. -l) and (3.4) In class: Find the Least Squares line through the population data: (it may simplifyr things to consider 1950...

Problems 1. You have been given code for generating polynomial interpolants by inverting the Vandermonde matrix all using equispaced points on 1,1 You will be interpolating the Runge function f(x)...

Consider a three-year mortgage with annual payments in arrears. Suppose the probability of default is 1% in the first year and 5% each year thereafter given that default has not occurred previously....

The simply-supported beam ABCD is loaded by a weight W = 27 kN through the arrangement shown in the figure. The cable passes over a small frictionless pulley at B and is attached at E to the end of...

Systematic risk is defined as: Multiple Choice e - the total risk of an individual security. the risk unique to a firm's management. diversifiable risk. Ssset - specific risk.

Monsoon Inc. is considering bidding on a government project. To do the project, the company must make an initial investment of $9 million to purchase the necessary equipment. The project will last...