Answer:-
1.
x2−y2=0If z≥0,x2>y2, then f(x,y,z)≥0.
If z≥0,x2<y2, then f(x,y,z)≤0.
If z≤0,x2>y2, then f(x,y,z)≤0.
If z≤0,x2<y2, then f(x,y,z)≥0.
Range: (−∞,∞)
2. Let u(x)=xsin(x1)
If x→±∞, then u(x)→1−
u′=sin(x1)−x1cos(x1)u′=0=>sin(x1)−x1cos(x1)=0x1=−0.22255,x2=0.22255u(−0.22255)=u(0.22255)≈−0.21723−0.21723≤u<1,x=0−0.21723−0.21723≈−0.4345
Range: [−0.4345,2)
3.
4−x2−y2−z2>00≤x2+y2+z2<4Then
0<4−x2−y2−z2≤2Range: [21,∞)
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