Chapter 3: Derivatives - Section 3.9 - Linearization and Differentials - Exercises 3.9 - Page 174: 6

a. $L(x)=x$ b. $L(x)=1$ c. $L(x)=x$

a. $f(x)=sin(x)$, $f(0)=sin(0)=0$, $f'(x)=cos(x)$, $f'(0)=cos(0)=1$, The linearization at $x=0$ is $L(x)=f(0)+f'(0)(x-0)=0+(x)=x$ b. $f(x)=cos(x)$, $f(0)=cos(0)=1$, $f'(x)=-sn(x)$, $f'(0)=-sin(0)=0$, The linearization at $x=0$ is $L(x)=f(0)+f'(0)(x-0)=1+0(x)=1$ c. $f(x)=tan(x)$, $f(0)=tan(0)=0$, $f'(x)=sec^2(x)$, $f'(0)=sec^2(0)=1$, The linearization at $x=0$ is $L(x)=f(0)+f'(0)(x-0)=0+(x)=x$