×
Log in to StudySoup
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.5 - Problem 45e
Join StudySoup for FREE
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.5 - Problem 45e

Already have an account? Login here
×
Reset your password

# Errors in approximations Suppose is to be approximated

ISBN: 9780321570567 2

## Solution for problem 45E 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

4 5 1 306 Reviews
18
0
Problem 45E

Errors in approximations Suppose is to be approximated near ? x = 8. Find the linear approximat?ion t?o f ? at ?x = 8. Then, complete the following table, showing the errors in various approximations. Use a calculator to obtain the exact values. The percent error is 100 • | approximation - exact | / | exact |. Comment on the behavior of the errors as ?x approaches 8.

Step-by-Step Solution:
Step 1 of 3

SOLUTION STEP 1 .The linear approximation formula is given by y = L(x) = f(a)+f (a)(xa) Given f(x) = and a = 8. 3 f(a) = 8 = 2 Then f (x) = 12 (a) = 12 = 1 3x3 3(8) 12 Therefore 1 L(x) = 2+ (128) x Linear Exact Percent approx value error 8.1 2.0083 2.0082 0.00497 8.0 2.000833 2.0008 0.00016 1 3 3 8.0 2.000083 2.0000 0.00001 01 33 83 6 8.0 2.000008 2.0000 0.00000 00 333 083 16 1 7.9 1.999991 1.9999 0.00008 99 66 9 3 9 7.9 1.999916 1.9999 0.00083 99 6 7.9 1.999166 1.9991 0.0033 9 7.9 1.9916 1.9916 0.003 We can find that as x approaches to 8 the error is almost equal to 0

Step 2 of 3

Step 3 of 3

#### Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Errors in approximations Suppose is to be approximated