Chapter 4 - Applications of the Derivative - 4.1 Linear Approximation and Applications - Exercises - Page 174: 66

$3.46$ %

Let $f(x)$ = $\ln(1+x)$, $a=0$ $f(a)$ = $f(0)$ = $0$ $f'(x)$ = $\frac{1}{1+x}$ $f'(a)$ = $f'(0)$ = $1$ $L(x)$ = $f'(a)(x-a)+f(a)$ $L(x)$ = $1(x-0)+0$ = $x$ Percentage error = $|\frac{\ln1.07-1}{\ln1.07}|\times100$ = $3.46$ %