×
×

# 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 1 264 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...

Step 2 of 3

Step 3 of 3

##### ISBN: 9780321570567

Unlock Textbook Solution