At what points is the given function continuous?
-$f ( x , y ) = \tan ( x + y )$
A) All $( x , y ) \neq \left( \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$
B) All $( x , y ) \neq ( 0,0 )$
C) All $( x , y )$ such that $x + y \neq \frac { ( 2 n + 1 ) \pi } { 2 }$, where $n$ is an integer
D) All ( $x , y )$

Question

Quizplus · Accepted Answer

The function is continuous except when the denominator of the tangent function becomes undefined, which happens when $x+y = \frac{(2n+1)\pi}{2}$ where $n$ is an integer. Therefore, the function is continuous for all points where this condition does not hold, which is option C.

At What Points Is the Given Function Continuous? - f(x,y)=tan⁡(x+y)f ( x , y ) = \tan ( x + y )f(x,y)=tan(x+y)

At What Points Is the Given Function Continuous?
- $f ( x , y ) = \tan ( x + y )$