Answer
$$0.000636$$
Work Step by Step
$f_x(0,0,\dfrac{\pi}{4})$
$=-\sqrt 2 \sin x \sin (y+z)$
$ =-\sqrt 2 \sin (0) \sin (0+(\pi/4))=0$
$f_y(0,0,\dfrac{\pi}{4})$
$=\sqrt 2 \cos x \cos (y+z)$
$=-\sqrt 2 \sin (0) \sin (0+(\pi/4))$
$=0$
$f_z(1,1,0)$
$=2y-3x=2(1)-3(1)$
$=-1$
Error:
$|E(x,y,z)| \leq \dfrac{1}{2} (\sqrt 2) [ |x-0| +|y-0|+|z-\dfrac{\pi}{4}|)^2$
or, $$ E \leq \dfrac{\sqrt 2}{2} (0.01+0.01+0.01)^2 =0.000636$$
