At what points is the given function continuous?
-$$f ( x , y , z ) = \frac { e ^ { x } } { e ^ { y + z } }$$
A) All $( x , y , z )$ in the first octant
B) All $( x , y , z )$
C) All $( x , y , z )$ such that $x \geq 0$ and $y + z \geq 0$
D) All $( x , y , z )$ such that $x - y - z \geq 0$

Question

Quizplus · Accepted Answer

The function $f(x, y, z) = \frac{e^x}{e^{y+z}}$ is continuous for all real numbers because the exponential function is continuous everywhere, and there are no points where the denominator becomes zero (since $e^{y+z}$ is never zero).

At What Points Is the Given Function Continuous? - f(x,y,z)=exey+zf ( x , y , z ) = \frac { e ^ { x } } { e ^ { y + z } }f(x,y,z)=ey+zex​

At What Points Is the Given Function Continuous?
- $f ( x , y , z ) = \frac { e ^ { x } } { e ^ { y + z } }$