Hey guys,
How do I find the range of f(x,y)=sqrt(9-x^2-y^2)?
Thanks for the help!
How do I find the range of f(x,y)=sqrt(9-x^2-y^2)
√9−x2−y2=√9−(x2+y2)So for real solutionsx2+y2≤9−3≤x≤3and−3≤y≤3The range is −3≤y≤3
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
Thanks Chris,
I guess it was the the restriction on z scores that were wanted. :/