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Hey guys,

 

How do I find the range of f(x,y)=sqrt(9-x^2-y^2)?

 

Thanks for the help!

 Aug 4, 2017
 #1
avatar+118696 
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How do I find the range of f(x,y)=sqrt(9-x^2-y^2)

 

 

9x2y2=9(x2+y2)So for real solutionsx2+y293x3and3y3The range is 3y3

 Aug 4, 2017
 #2
avatar+130466 
+2

 

f (x,y)  = √ [ 9 - x ^2 - y^2 ]  = √ [ 9 - ( x ^2 + y^2) ]

 

We have a 3D surface here

 

Let  f(x,y)  = z

 

In real terms, the minimum for z, 0, will be achieved when x^2 + y^2   = 9

 

And the maximum for z, 3, will be achieved when   x , y   = 0 

 

And the range of z will be      0 ≤ z ≤ 3

 

 

cool cool cool

 Aug 4, 2017
edited by CPhill  Aug 4, 2017
 #3
avatar+118696 
0

Thanks Chris,

I guess it was the the restriction on z scores that were wanted.   :/

Melody  Aug 7, 2017

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