×
Log in to StudySoup
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.5 - Problem 9e
Join StudySoup for FREE
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.5 - Problem 9e

Already have an account? Login here
×
Reset your password

Answer: Linear approximation a. Write The equation of the

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

Solution for problem 9E Chapter 4.5

Calculus: Early Transcendentals | 1st Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

4 5 1 351 Reviews
19
3
Problem 9E

Linear approximation a. Write The equation of the line that represents the linear approximation to the following functions at the given point a. b. Graph the function and the linear approxim?ation near x = ?a. c. Use the linear approximation to estimate the given function value. d. Compute the percent error in your ? approximation: 100 • lapprox-exact| / |exact| ? ? ? ? f(?x)? = ln(1 + ?x); ?a =0; ?f(0.9)

Step-by-Step Solution:
Step 1 of 3

Solution 9E STEP 1 Given f(x) = ln(1 + x);a = 0;f(0.9) 1 f x) = 1+x (a). Equation of the line of linear approximation y = L(x) = f(a) + f (a)(x ) Thus f(a) = ln (1 + 0) = ln 1 = 0 f (a) = 1 = 1 1+0 Therefore y = L(x) = f(a) + f (a)x a) y = 0 + 1(x 0) = x Thus we get y = x STEP 2 (b).Graph the function and the linear approximation near x = a. STEP 3 (c). Use the linear approximation to estimate the given function value. We have f(0.9) L(0.9) 0.9 Therefore f(0.9) 0.9 STEP 4 (d). |approximate exact| Compute the percent error in your approximation: 100 × |exact| We get the exact value ,f(0.9)= ln(1 + 0.9) = 0.641 0.90.641 Then percent error = 100 × | |0.641|| = 40%

Step 2 of 3

Chapter 4.5, Problem 9E is Solved
Step 3 of 3

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

Other solutions

People also purchased

Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Answer: Linear approximation a. Write The equation of the