Let u D ui C vj be a unit vector, and let fu.t / D f .a C tu
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Let u D ui C vj be a unit vector, and let fu.t / D f .a C tu; b C tv/ be the single-variable function obtained by restri
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Let u D ui C vj be a unit vector, and let fu.t / D f .a C tu; b C tv/ be the single-variable function obtained by restricting the domain of f .x; y/ to points of the straight line through .a; b/ parallel to u. If fu.t / is continuous at t D 0 for every unit vector u, does it follow that f is continuous at .a; b/? Conversely, does the continuity of f at .a; b/ guarantee the continuity of fu.t / at t D 0? Justify your answers.
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