#### Answer

$$0.0222$$

#### Work Step by Step

$$f_x=e^x \cos y \\ f_x(0,0)=e^{0} \cos 0=1 \\ f_y(x,y) =-e^x \sin y \\ f_{y}(0,0) =0 \\ f_{xx}(x,y)=-e^x \cos y \\ f_{yy}(x,y)=-e^x \cos y \\ f_{xy}(x,y) =-e^x \sin y$$
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$