Question

find range of sqrt(25-x^2-y^2-z^2)

Answer 1

\[\sqrt{25-x^{2}-y^{2}-z^{2}}\]

Answer 2

25 - x^2 - y^2 - z^2 ≥ 0
25 ≥ x^2 + y^2 + z^2
5^2 ≥ x^2 + y^2 + z^2

so it's a sphere with the radius less than or equal to 5

Answer 3

actually it's the upper hemisphere

Answer 4

ok, just use sphere formula to find the range?? can't be calculate by using function way??

Answer 5

actually this is the multivariable function question

Answer 6

f(x,y,z)=sqrt(25-x^2-y^2-z^2)

Answer 7

if that's the case, 0 <= f(x,y,z) <= 5

Answer 8

ya, but how to calculate??

Answer 9

still using sphere formula??

Answer 10

well it's not sphere anymore. It's like a 4-dimension "sphere"

Answer 11

quite blur.... is there any method of calculation??

Answer 12

well, i'm certian there are.

Answer 13

sqrt(r^2 - x^2) is a upper semi-circle and the range is 0 <= y = < r
sqrt(r^2 - x^2 - y^2) is an upper hemisphere, range: 0 <= z <= r
sqrt(r^2 - x^2 - y^2 - z^2) (this is 4-d), regardless, range: 0 <= f(x,y,z) <= r

Answer 14

ok. thx a lot, understand ald... ^^