×
×

# Linear approximation a. Write The equation of the line ISBN: 9780321570567 2

## Solution for problem 7E 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 1 359 Reviews
20
3
Problem 7E

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 approximation near x? = a ? . c. Use the linear approximation to estimate the given function value. d. Compute the percent error in your approximation:? 100 • l approx-exact | / |exact| f?? ?) = 12 ?? ? a = 2; ?? 2.1)

Step-by-Step Solution:
Step 1 of 3

SOLUTION STEP 1 Given f(x) = 12 x ;a = 2;f(2.1) f(x) = 2x (a). Equation of the line of linear approximation y = L(x) = f(a) + f(a)(x a) 2 Thus f(a) = 12 2 = 12 4 = 8 f(a) = 2 × 2 = 4 Therefore y = L(x) = f(a) + f(a)(x a) y = 8 + 4(x a) = 8 4x + 4a = 8 4x + 4 × 2 = 8 4x + 8 = 16 4x Thus we get y = 16 4x STEP 2 (b).Graph the function and the linear approximation...

Step 2 of 3

Step 3 of 3

##### ISBN: 9780321570567

Unlock Textbook Solution