Chapter 13 - Section 13.6 - Tangent Planes and Differentials - Exercises - Page 729: 38

$0.0832$

$f_x=x^{-1} \\ \implies f_x(1,1)=1^{-1}=1$ Next, $f_y(x,y) =y^{-1} \\ \implies f_{y}(1,1) =1^{-1}=1$ $f_{xx}(x,y)=-x^{-2}; f_{yy}(x,y)=-y^{-2}$ and $f_{xy}(x,y) =0$ The error can be found as: $|E(x,y)| \leq \dfrac{1}{2} \times (1.04) [ |x-1| +|y-1|)^2$ $\implies E \leq \dfrac{1.04}{2} \times (0.2+0.2)^2 =0.0832$