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

May 2009
34
0
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..(Hi)
 

Ackbeet

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Jun 2010
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Try taking sections of it. If you plug in different values of \(\displaystyle z\), what do you get in the \(\displaystyle xy\) plane? Are there values of \(\displaystyle z\) that are not allowed?
 
May 2009
34
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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!(Smirk)
 
Nov 2009
130
24
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:

 
May 2009
34
0
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!! (Rofl)