Question

Find the domain of function and draw the graphs of domain function?
(a) 𝒇(𝒙, 𝒚, 𝒛) = 𝟏 √𝟑𝟔−𝟒𝒙
𝟐−𝟗𝒚𝟐−𝒛 𝟐 . (b) 𝒇(𝒙, 𝒚, 𝒛) =
√𝟏𝟔 − 𝒙 𝟐 − 𝒚 𝟐 − 𝒛 𝟐 𝟑 .

Accepted Answer

a) frac{1}{ sqrt{36-4x^2-9y^2-z^2}} for the solution to be defined, the denominator cannot be zero and the radicand cannot be negative. 36-4x^2-9y^2-z^2>0 n4x^2+9y^2+z^2<36 n text{domain of f }={(x,y,z) in R^3 : 4x^2+9y^2+z^2<36} n frac{1}{9}x^2+ frac{1}{4}y^2+ frac{1}{36}z^2<1 which is an ellipsoid equation of x radius = 3 y radius = 2 z radius = 6 b) { sqrt{16-x^2-9y^2-z^2}} for the solution to be defined, the radicand cannot be zero and cannot be negative {16-x^2-y^2-z^2}>0 nx^2+y^2+z^2<16 n text{domain of f }={(x,y,z) in R^3 : x^2+y^2+z^2<16} n frac{1}{16}x^2+ frac{1}{16}y^2+ frac{1}{16}z^2<1 which is an ellipsoid equation of x radius = 4 y radius = 4 z radius = 4

Question #252676

Expert's answer

Answer in progress...