Problem about Differentials with non Independent Variables

Jomo said:
The constraint is in the x-y plane where z=0 always.
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Thanks for your answer, but I'm still confused. The constrain is in the x-y plane, I agree, but this means that (may be I'm wrong) function "w" can take any "z" values, with the condition that the constraining function (the one in x-y plane) be fulfilled, and that (as far as I can see) does not implies that "z=0"...
 
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Yes, you are wrong! The "xy-plane" is the plane, in a three dimensional xyz coordinate system, containing both the x-axis and the y- axis. Every point on the x-axis is (x, 0, 0) and every point on the y- axis is (0, y, 0). The xy-plane is specifically the set of points (x, y, 0). In the xy-plane, z= 0.
 
HallsofIvy said:
Yes, you are wrong! The "xy-plane" is the plane, in a three dimensional xyz coordinate system, containing both the x-axis and the y- axis. Every point on the x-axis is (x, 0, 0) and every point on the y- axis is (0, y, 0). The xy-plane is specifically the set of points (x, y, 0). In the xy-plane, z= 0.
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But I see no mention of the xy-plane in the problem. It just puts a constraint on x and y without mention of z. Is there something that would have been explained in the text, such that such a constraint, in this context, implies the xy-plane?
 
Dr.Peterson said:
But I see no mention of the xy-plane in the problem. It just puts a constraint on x and y without mention of z. Is there something that would have been explained in the text, such that such a constraint, in this context, implies the xy-plane?
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I agree with you. That's may be the explanation: The enunciate of the problem has forgotten to tell, in one or another way, that "z=0".
 
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