Chapter 13 - Section 13.6 - Tangent Planes and Differentials - Exercises - Page 729: 33

$0.06$

$f_x= 2x-3y \implies f_x(2,1)=1$ and $f_y(x,y) =-3x \implies f_{y}(2,1) =-3 (2)=-6$ $f_{xx}(2,1)=2; f_{yy}(x,y)=0$ and $f_{xy}(x,y) =-3$ $L(x,y)=3+1(x-2) -6(y-1) =7+x-6y$ The error can be found as: $|E(x,y)| \leq \dfrac{1}{2} \times 3 [ |x-2| +|y-1|)^2$ $\implies E \leq \dfrac{3}{2} \times (0.1+0.1)^2 =0.06$