Chapter 13 - Section 13.6 - Tangent Planes and Differentials - Exercises - Page 729: 35

$0.08$

$f_x= \cos y \\ \implies f_x(0,0)=\cos 0=1$ Next, $f_y(x,y) =1-x \sin y \\ \implies f_{y}(0,0) =1-0 \sin (0)=1$ $f_{xx}(x,y)=0; f_{yy}(x,y)=-x \ cos y$ and $f_{xy}(x,y) =- \sin y$ The error can be found as: $|E(x,y)| \leq \dfrac{1}{2} \times 1 [ |x-0| +|y-0|)^2$ $\implies E \leq \dfrac{1}{2} \times (0.2+0.2)^2 =0.08$