1. ## x^2+y^2+z=1 sketch

Hi,
I'm having difficulty with this eqatuion and wanted to know what is this equation? is it a cone? and how would i sketch the points...Thank you for your time..

2. Try taking sections of it. If you plug in different values of $z$, what do you get in the $xy$ plane? Are there values of $z$ that are not allowed?

3. Its actually to verify stokes theorem...x^2+y^2+z-1=0 where z is equal to or larger than 0...I just wanted to know how to sketch it and how to go about it. Thank you!

4. x^2+y^2+z-1=0

Now x^2+y^2-1=-z

and z=1-(x^2+y^2)

Do you know what is z1=x^2+y^2. It is paraboloid.

Its sections x^2+y^2=k or x^2+y^2=Sqrt[k]^2 are circles with radius Sqrt[k].

So first draw the paraboloid. Then reflect it around the z-axis (just turn it upside down), and finally move it for 1 unit up in the z-axis.

Regards.

P.S The graph that you need will look something like this:

5. I see..thank you for making it clearer..I also have a question regarding the polar co-ordinates for a paraboloid and its boundary conditions..and also..how to convert them for the stokes theorem..Thank you!!