Given a function f .x; y/ and a point .a; b/ in its domain,
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Given a function f .x; y/ and a point .a; b/ in its domain, define single-variable functions g and h as follows: g.x/ D
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Given a function f .x; y/ and a point .a; b/ in its domain, define single-variable functions g and h as follows: g.x/ D f .x; b/; h.y/ D f .a; y/: If g is continuous at x D a and h is continuous at y D b, does it follow that f is continuous at .a; b/? Conversely, does the continuity of f at .a; b/ guarantee the continuity of g at a and the continuity of h at b? Justify your answers.
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