# Thread: Limits by definition - 2 variables function

1. ## Limits by definition - 2 variables function

lim_(x,y)-->(2,1) f(x,y)=3

where f(x,y)= (x+y) / (x-y)

2. Originally Posted by johnnashfcup

lim_(x,y)-->(2,1) f(x,y)=3

where f(x,y)= (x+y) / (x-y)

The numerator and denominator are both continuous functions, so the only place where $f(x, y)$ is not continuous is where the denominator $= 0$. This does not occur at $(x, y) = (2, 1)$, so you can just use direct substitution.
$\lim_{(x, y) \to (2, 1)}\frac{x + y}{x - y} = \frac{2 + 1}{2 - 1}$
$= \frac{3}{1}$
$= 3$.