Chapter 14: Partial Derivatives - Section 14.6 - Tangent Planes and Differentials - Exercises 14.6 - Page 835: 37

$$0.0222$$

$$f_x=e^x \cos y \\ f_x(0,0)=e^{0} \cos 0=1 \\ f_y(x,y) =-e^x \sin y \\ f_{y}(0,0) =0 \\ f_{xx}(x,y)=-e^x \cos y \\ f_{yy}(x,y)=-e^x \cos y \\ f_{xy}(x,y) =-e^x \sin y$$ Error: $|E(x,y)| \leq \dfrac{1}{2} (1.11) [ |x-0| +|y-0|)^2$ or, $ E \leq \dfrac{1.11}{2} (0.1+0.1)^2 =0.0222$