Chapter 4 - Applications of the Derivative - 4.1 Linear Approximation and Applications - Exercises - Page 174: 67

$0.0073$%

Let $f(x) = e^{x}, a=0$ $f(a) = f(0) = e^{0} = 1$ $f'(x) = e^{x}$ $f'(a) = f'(0) = 1$ $L(x) = f'(a)(x-a)+f(a)$ $L(x) = 1(x-0)+1$ = $x+1$ $L(-0.012) = -0.012+1 = 0.988$ Percentage error = $|\frac{e^{-0.012}-0.988}{e^{-0.012}}|\times100$% = $0.0073$%