a. Explanation Given: The function f ( x ) = ln ( 1 + x ) and x = − 0.2 , − 0.1 , 0.0 , 0.1 , and 0.2 . The Taylor polynomials, p 1 ( x ) = x and p 2 ( x ) = x − x 2 2 . Calculation: Use the online calculator and obtain the absolute error. The value of | ln ( 1 + x ) − p 1 ( x ) | computed as follows, x ln ( 1 + x ) p 1 ( x ) = x | ln ( 1 + x ) − p 1 ( x ) | −0.2 −0.2231 −0.2 2.3143 × 10 − 2 −0.1 −0.1054 −0.1 5.3605 × 10 − 3 0.0 0 0.0 0 0.1 0.0953 0.1 4.6898 × 10 − 3 0.2 0.1823 0.2 1.7679 × 10 − 2 The value of | ln ( 1 + x ) − p 2 ( x ) | computed as follows, x p 2 ( x ) = x − x 2 2 ln ( 1 + x ) | ln ( 1 + x ) − p 2 ( x ) | −0.2 ( − 0.2 ) − ( − 0.2 ) 2 2 = − 0.22 −0.2231 3.1436 × 10 − 3 −0 b. To determine To describe: The error varying with x in each column and find the values of x largest and smallest in magnitude.

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 9.1, Problem 88E

To determine

To approximate: The absolute error to two significant digits at the given points.

To determine

To describe: The error varying with x in each column and find the values of x largest and smallest in magnitude.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.1, Problem 87E

Chapter 9.1, Problem 89E

Students have asked these similar questions

Use the Newton-Raphson following polynomial: f(x)=e* − x = 0 Now we need to evaluate f'(x)=-e* - 1 x-(x-)dx= (x) 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 0.2 method to find a root of the Newton Raphson Formulation f (x₁) ƒ'(x;) Xi+1 = Xi 0.4 0.6 0.8 = X i e -Xi -e -Xi -X - 1

Taylor polynomial for f(x)=In x to approximate f(1.15) with x0=1, and n=5

Taylor polynomial P1(x) of f(x)=cos((4-2x)·t) at the point X0=1. Find the Taylor polynomial, the Taylor remainder, and give an appropriate upper bound on the error in approximating f(x) with P1(x) at X=1.3. In giving the polynomial, use the equation editor to enter your answer.

Chapter 9 Solutions

Calculus: Early Transcendentals (2nd Edition)

Ch. 9.1 - Suppose you use a second-order Taylor polynomial...Ch. 9.1 - Does the accuracy of an approximation given by a...Ch. 9.1 - The first three Taylor polynomials for f(x)=1+x...Ch. 9.1 - Prob. 4E Ch. 9.1 - How is the remainder Rn(x) in a Taylor polynomial...Ch. 9.1 - Explain how to estimate the remainder in an...Ch. 9.1 - Linear and quadratic approximation a. Find the...Ch. 9.1 - Linear and quadratic approximation a. Find the...Ch. 9.1 - Linear and quadratic approximation a. Find the...Ch. 9.1 - Linear and quadratic approximation a. Find the...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

To approximate: The absolute error to two significant digits at the given points.

Solution Summary: The author explains how to approximate the absolute error to two significant digits at the given points.

Videos

To approximate: The absolute error to two significant digits at the given points.

To describe: The error varying with x in each column and find the values of x largest and smallest in magnitude.

Want to see the full answer?

Chapter 9 Solutions