Solution Found!

Math / Numerical Analysis 10 / Chapter 3.1 / Problem 1

Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden

Change Question

For the given functions /(a), let Aq = 0, A

Chapter 3, Problem 1

(choose chapter or problem)

Get Unlimited Answers

QUESTION:

For the given functions /(a), let Aq = 0, A| = 0.6, and X2 = 0.9. Construct interpolation polynomials of degree at most one and at most two to approximate /(0.45) and find the absolute error. a. /(a) = cos a c. /(a) = ln(A 4- 1) b. /(a) = \/1+a d. /(a) = tan a

Questions & Answers

QUESTION:

For the given functions /(a), let Aq = 0, A| = 0.6, and X2 = 0.9. Construct interpolation polynomials of degree at most one and at most two to approximate /(0.45) and find the absolute error. a. /(a) = cos a c. /(a) = ln(A 4- 1) b. /(a) = \/1+a d. /(a) = tan a

ANSWER:

Step 1 of 6

(a)

The linear Langrange interpolating polynomial through and is given as

At nodes and , the corresponding function values are

Therefore, the polynomial is determined as

The approximation of would be

So the absolute error is

Study Tools You Might Need

Chapter: 1 Problem: 66P

An Introduction to Thermal Physics 1
Problem 66P In analogy with the thermal conductivity, derive an approximate formula for the viscosity of an ideal gas in terms of its density, mean free path, and average thermal speed. Show explicitly that the viscosity Is Independent of pressure and proportional to the square root of the temperatur

Chapter: 1 Problem: 1.1-6

Probability and Statistical Inference 9
PROBLEM 6E If P(A) = 0.4, P(B) = 0.5, and P(A?B) = 0.3, find (a) P(A ? B), (b) P(A ? B' ), and (c) P(A' ? B' ).

Chapter: 1 Problem: 1.34

Organic Chemistry 2
Draw structures for all constitutional isomers with the followingmolecular formulas:(a) C4H10 (b) C5H12 (c) C6H14(d) C2H5Cl (e) C2H4Cl2 (f) C2H3Cl3

Chapter: 1 Problem: 1

Fundamentals of Physics: 9
Earth is approximately a sphere of radius 6.37 X 106 m. What are (a) its circumference in kilometers, (b) its surface area in square kilometers, and (c) its volume in cubic kilometers?

Chapter: 0 Problem: 1

Biology 8
Vertebrates and tunicates share a. jaws adapted for feeding. b. a high degree of cephalization. c. the formation of structures from the neural crest. d. an endoskeleton that includes a skull. e. a notochord and a dorsal, hollow nerve cord

Chapter: 3 Problem: 3.8

Chemistry: The Molecular Nature of Matter and Change - Standalone book 7
Calculate the molar mass of each of the following: (a) Sr(OH)2 (b) N2O3 (c) NaClO3 (d) Cr2O3

Chapter: 0 Problem: 4

Economics: Principles and Practices, Reading Essentials and Study Guide, Workbook 1
How does diminishing marginal utility affect demand?

Chapter: 16 Problem: 6

Human Biology 11
Label the parts of the female reproductive system and list their functions.

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

×

Register

Sign up for access to all content on our site!

Or login if you already have an account