Continuity of two variable function

[boneill3]

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]

Hi Brendan!

(have a delta: δ and an epsilon: ε )

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]

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?