continuity of two variable function

**boneill3** · Jun18-09, 06:52 AM

Hi Guy's I was wondering if anyone knows of a good link to explain the proof

That if a function of two variables f(x,y) is differentiable at (x,y) than f(x,y) is continuous at (x,y)

regards
Brendan

**tiny-tim** · Jun18-09, 08:55 AM

Hi Brendan!

(have a delta: δ and an epsilon: ε

)

Originally Posted by boneill3

That if a function of two variables f(x,y) is differentiable at (x,y) than f(x,y) is continuous at (x,y)

That looks like a standard δ,ε proof …

have a go, using the definitions of differentiable and continuous, and show us what you get.

**HallsofIvy** · Jun18-09, 10:09 AM

Crucial point: the definition of the derivative involves taking the limit of a fraction in which the denominator always goes to 0. What has to happen to the numerator?