# 2 Variable Continuity

Calculus Level 3

Suppose that $$f(x,y)$$ satisfies the following conditions:

• For all $$X$$, the function $$f( X, y )$$ is continuous in $$y$$.
• For all $$Y$$, the function $$f ( x, Y)$$ is continuous in $$x$$.

Must the function $$f(x,y)$$ be continuous?

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