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## Homework Statement

f(x,y) is a two variables function for which the hypothesis of Schwarz's theorem hold in a point (a,b).

is f continuous in (a,b)?

## The Attempt at a Solution

I think it is, because being the two mixed partials continuous in (a,b) the function is twice differentiable, and therefore globally Lipschitz, which implies continuity.

Am I right?