Solved: Linear and quadratic approximationa. Find the

ISBN: 9780321570567 2

Solution for problem 8E Chapter 9.1

Calculus: Early Transcendentals | 1st Edition

Calculus: Early Transcendentals | 1st Edition

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Problem 8E

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.

, a = 4; approximate

Step-by-Step Solution:

Solution 8E

Step 1:

We need to find the linear and quadratic approximating polynomial for $f(x)=\sqrt{x}\ at\ a=4$

The linear approximation for $f$ at $a$ is given by $L(x)=f(a)+f\ '(a)(x-a)$

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

$Q(x)\ =f(a)\ +\ f'(a)\ (x\ -\ a)\ +\ 1/2\ f''(a)\ (x\ -\ a{)}^{2}=L(x)+1/2\ f''(a)\ (x\ -\ a{)}^{2}$

Step 2 of 4

Step 3 of 4

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