1.f(x,y,z)=x2−y2z
dom(f)={(x,y,z)∈R3 ∣ x2−y2=0}={(x,y,z)∈R3 ∣ (x−y)(x+y)=0}=R3∖{(x,x,z),(x,−x,z)) ∣ x,z∈R}.
2. f(x,y)=xsin(x1)+ysin(y1)
dom(f)={(x,y)∈R2 ∣ x=0,y=0}=R2∖{(x,0),(0,y) ∣ x,y∈R}.
3. f(x,y,z)=4−x2−y2−z21
dom(f)={(x,y,z)∈R3 ∣ 4−x2−y2−z2>0}={(x,y,z)∈R3 ∣ x2+y2+z2<4}.
Comments
Leave a comment