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Linear and quadratic approximationa. Find the | Ch 9.1 - 12E

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 12E Chapter 9.1

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 12E

Problem 12E

Linear and quadratic approximation

a. Find the linear approximating polynomial for the following functions centered at the given point a.

b. Find the quadratic approximating polynomial for the following functions centered at the given point a.

c. Use the polynomials obtained in parts (a) and (b) to approximate the given quantity.

f(x)= tan−1 x, a = 0; approximate tan−1 0.1.

Step-by-Step Solution:

Solution 12E

Step 1:

We need to find the linear and quadratic approximating polynomial for

The linear approximation for  at is given by

The Quadratic Approximation for a function y = f(x) based at a point a is given by

Step 2 of 4

Chapter 9.1, Problem 12E is Solved
Step 3 of 4

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Linear and quadratic approximationa. Find the | Ch 9.1 - 12E