Answer
$0.00135$
Work Step by Step
$f_x=y-3z $ and $f_x(1,1,0)=1-3(0)=1$
$f_y =x+2z$ and $f_{y}(1,1,0) =1+(2)(0)=1$ and $f_z(1,1,0)=2y-3x=(2)(1)-(3)(1)=-1$
$$f_{xx}=0 \\f_{yy}=0 \\ f_{zz} =0 \\ f_{xy}=1 \\ f_{xz}=-3 \\ f_{yz}=2$$
Error:
$|E(x,y,z)| \leq \dfrac{1}{2} \times (3) [ |x-1| +|y-1|+|z-0|)^2$
or, $$E \leq \dfrac{3}{2} \times (0.01+0.01+0.01)^2 =0.00135$$
