Answer
a) $g(\pi,0)=0$
b) $g(\frac{\pi}{2},\frac{\pi}{4})=\frac{\pi\sqrt{2}+\pi}{4}$
c) $g(0,y)=0$
d) $g(x,y+h)=x\sin (y+h)+(y+h)\sin x$
Work Step by Step
$g(x,y)=x\sin y+y\sin x$
a) $g(\pi,0)=\pi \sin 0+0\sin \pi=0$
b) $g(\frac{\pi}{2},\frac{\pi}{4})=\frac{\pi}{2}\sin \frac{\pi}{4}+\frac{\pi}{4}\sin \frac{\pi}{2}=\frac{\pi\sqrt{2}+\pi}{4}$
c) $g(0,y)=0\sin y+y\sin 0=0$
d) $g(x,y+h)=x\sin (y+h)+(y+h)\sin x$