Question

Describe the domain of \( f \) in words. (a) \( f(x, y)=x e^{-\sqrt{y+2}} \) (b) \( f(x, y, z)=\sqrt{25-x^{2}-y^{2}-z^{2}} \) (c) \( f(x, y, z)=e^{x y z} \) (a) \( f(x, y)=\frac{\sqrt{4-x^{2}}}{y^{2}+3} \) (b) \( f(x, y)=\ln (y-2 x) \) (c) \( f(x, y, z)=\frac{x y z}{x+y+z} \)

          Describe the domain of \( f \) in words.
(a) \( f(x, y)=x e^{-\sqrt{y+2}} \)
(b) \( f(x, y, z)=\sqrt{25-x^{2}-y^{2}-z^{2}} \)
(c) \( f(x, y, z)=e^{x y z} \)
(a) \( f(x, y)=\frac{\sqrt{4-x^{2}}}{y^{2}+3} \)
(b) \( f(x, y)=\ln (y-2 x) \)
(c) \( f(x, y, z)=\frac{x y z}{x+y+z} \)

Describe the domain of f in words.
(a) f(x, y)=x e^-√(y+2)
(b) f(x, y, z)=√(25-x^2-y^2-z^2)
(c) f(x, y, z)=e^x y z
(a) f(x, y)=(√(4-x^2))/(y^2+3)
(b) f(x, y)=ln (y-2 x)
(c) f(x, y, z)=(x y z)/(x+y+z)

Added by Victoria H.

Calculus Early Transcendentals

Howard Anton, Irl Bivens, Stephen Davis 9th Edition

Chapter 13

Instant Answer

Solved by Expert Abigail Martyr

08/11/2020

Step 1

This involves considering any restrictions imposed by operations such as square roots, logarithms, and division. (a) \( f(x, y) = x e^{-\sqrt{y+2}} \) - The expression \(-\sqrt{y+2}\) requires that the argument of the square root, \(y+2\), be non-negative. Show more…

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