Range, functions, multivariable

Dec 2015
1,084
169
Earth
Find the range of functions below :
(1) \(\displaystyle \: F(x,y)=e^{-x-y}(x+y^2 )\; , \: x,y \in \mathbb{R}\).

(2) \(\displaystyle \: F(x,y,z)=\dfrac{xyz}{x+y+z}\; , \: x,y,z \in \mathbb{N}\).

(3) \(\displaystyle \: F(t)=te^{-t^2 } \; , \: t\in [0,1]\).
 

romsek

Math Team
Sep 2015
2,967
1,676
USA
1) $(-\infty, \infty)$

2) $\left[\dfrac 1 3, \infty)\right]$

3) $\left[0, \dfrac{1}{\sqrt{2}}\right]$
 
  • Like
Reactions: idontknow